{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0001","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235001,"parameters":{"n":7,"family":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0],[1,2,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0002","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235002,"parameters":{"n":7,"family":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,4,5,6],[1]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0003","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235003,"parameters":{"n":7,"family":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1],[2,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0004","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235004,"parameters":{"n":7,"family":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,4,5,6],[2]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0005","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235005,"parameters":{"n":7,"family":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2],[1,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0006","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235006,"parameters":{"n":7,"family":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4,5,6],[1,2]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0007","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235007,"parameters":{"n":7,"family":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2],[3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0008","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235008,"parameters":{"n":7,"family":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4,5,6],[3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0009","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235009,"parameters":{"n":7,"family":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,3],[1,2,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0010","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235010,"parameters":{"n":7,"family":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4,5,6],[1,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0011","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235011,"parameters":{"n":7,"family":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3],[2,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0012","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235012,"parameters":{"n":7,"family":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4,5,6],[2,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0013","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235013,"parameters":{"n":7,"family":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3],[1,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0014","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235014,"parameters":{"n":7,"family":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,4,5,6],[1,2,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0015","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235015,"parameters":{"n":7,"family":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3],[4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0016","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235016,"parameters":{"n":7,"family":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3,5,6],[4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0017","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235017,"parameters":{"n":7,"family":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,4],[1,2,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0018","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235018,"parameters":{"n":7,"family":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,5,6],[1,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0019","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235019,"parameters":{"n":7,"family":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4],[2,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0020","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235020,"parameters":{"n":7,"family":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,5,6],[2,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0021","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235021,"parameters":{"n":7,"family":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4],[1,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0022","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235022,"parameters":{"n":7,"family":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,5,6],[1,2,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0023","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235023,"parameters":{"n":7,"family":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4],[3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0024","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235024,"parameters":{"n":7,"family":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,5,6],[3,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0025","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-sigma-qualification；資料={\"n\":7,\"family\":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,has_empty,has_full,missing_complements,missing_unions,finite_countable_reduction,sigma] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], 是, 是, [], [], 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-sigma-qualification","seed":202610235025,"parameters":{"n":7,"family":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-sigma-qualification","semantic_template":"qf-mod23-measure-sigma-qualification/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4],[1,2,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0026","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235026,"parameters":{"n":7,"family":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0],[1,2,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0027","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235027,"parameters":{"n":7,"family":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,4,5,6],[1]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0028","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235028,"parameters":{"n":7,"family":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1],[2,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0029","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235029,"parameters":{"n":7,"family":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,4,5,6],[2]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0030","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235030,"parameters":{"n":7,"family":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2],[1,3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0031","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235031,"parameters":{"n":7,"family":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4,5,6],[1,2]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0032","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235032,"parameters":{"n":7,"family":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2],[3,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0033","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235033,"parameters":{"n":7,"family":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4,5,6],[3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0034","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235034,"parameters":{"n":7,"family":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,3],[1,2,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0035","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235035,"parameters":{"n":7,"family":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4,5,6],[1,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0036","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235036,"parameters":{"n":7,"family":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3],[2,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0037","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235037,"parameters":{"n":7,"family":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4,5,6],[2,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0038","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235038,"parameters":{"n":7,"family":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3],[1,4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0039","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235039,"parameters":{"n":7,"family":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,4,5,6],[1,2,3]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0040","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235040,"parameters":{"n":7,"family":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3],[4,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0041","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235041,"parameters":{"n":7,"family":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3,5,6],[4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0042","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235042,"parameters":{"n":7,"family":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,4],[1,2,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0043","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235043,"parameters":{"n":7,"family":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,5,6],[1,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0044","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235044,"parameters":{"n":7,"family":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4],[2,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0045","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235045,"parameters":{"n":7,"family":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,5,6],[2,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0046","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235046,"parameters":{"n":7,"family":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4],[1,3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0047","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235047,"parameters":{"n":7,"family":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,5,6],[1,2,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0048","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235048,"parameters":{"n":7,"family":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4],[3,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0049","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235049,"parameters":{"n":7,"family":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,5,6],[3,4]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0050","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-closure-inventory；資料={\"n\":7,\"family\":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]]}。請依 [n,family,missing_complements,missing_unions,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-closure-inventory","seed":202610235050,"parameters":{"n":7,"family":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],"domain":"Complete_finite_measure_space","operation":"measure-closure-inventory","semantic_template":"qf-mod23-measure-closure-inventory/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4],[1,2,5,6]],\"n\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0051","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[1,3],[2,3],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 1/3, 2/3, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 1/3, 2/3, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235051,"parameters":{"n":7,"family":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[1,3],[2,3],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0],[1,2,3,4,5,6]],\"n\":7,\"values\":[[0,1],[1,3],[2,3],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0052","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[2,5],[3,5],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 2/5, 3/5, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 2/5, 3/5, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235052,"parameters":{"n":7,"family":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[2,5],[3,5],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,4,5,6],[1]],\"n\":7,\"values\":[[0,1],[2,5],[3,5],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0053","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[3,7],[4,7],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 3/7, 4/7, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 3/7, 4/7, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235053,"parameters":{"n":7,"family":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[3,7],[4,7],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1],[2,3,4,5,6]],\"n\":7,\"values\":[[0,1],[3,7],[4,7],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0054","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[4,9],[5,9],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 4/9, 5/9, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 4/9, 5/9, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235054,"parameters":{"n":7,"family":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[4,9],[5,9],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,4,5,6],[2]],\"n\":7,\"values\":[[0,1],[4,9],[5,9],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0055","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[5,11],[6,11],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 5/11, 6/11, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 5/11, 6/11, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235055,"parameters":{"n":7,"family":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[5,11],[6,11],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2],[1,3,4,5,6]],\"n\":7,\"values\":[[0,1],[5,11],[6,11],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0056","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[6,13],[7,13],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 6/13, 7/13, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 6/13, 7/13, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235056,"parameters":{"n":7,"family":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[6,13],[7,13],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4,5,6],[1,2]],\"n\":7,\"values\":[[0,1],[6,13],[7,13],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0057","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[7,15],[8,15],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 7/15, 8/15, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 7/15, 8/15, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235057,"parameters":{"n":7,"family":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[7,15],[8,15],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2],[3,4,5,6]],\"n\":7,\"values\":[[0,1],[7,15],[8,15],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0058","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[8,17],[9,17],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 8/17, 9/17, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 8/17, 9/17, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235058,"parameters":{"n":7,"family":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[8,17],[9,17],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4,5,6],[3]],\"n\":7,\"values\":[[0,1],[8,17],[9,17],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0059","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[9,19],[10,19],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 9/19, 10/19, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 9/19, 10/19, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235059,"parameters":{"n":7,"family":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[9,19],[10,19],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3],[1,2,4,5,6]],\"n\":7,\"values\":[[0,1],[9,19],[10,19],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0060","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[10,21],[11,21],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 10/21, 11/21, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 10/21, 11/21, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235060,"parameters":{"n":7,"family":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[10,21],[11,21],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4,5,6],[1,3]],\"n\":7,\"values\":[[0,1],[10,21],[11,21],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0061","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[11,23],[12,23],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 11/23, 12/23, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 11/23, 12/23, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235061,"parameters":{"n":7,"family":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[11,23],[12,23],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3],[2,4,5,6]],\"n\":7,\"values\":[[0,1],[11,23],[12,23],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0062","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[12,25],[13,25],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 12/25, 13/25, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 12/25, 13/25, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235062,"parameters":{"n":7,"family":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[12,25],[13,25],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4,5,6],[2,3]],\"n\":7,\"values\":[[0,1],[12,25],[13,25],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0063","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[13,27],[14,27],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 13/27, 14/27, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 13/27, 14/27, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235063,"parameters":{"n":7,"family":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[13,27],[14,27],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3],[1,4,5,6]],\"n\":7,\"values\":[[0,1],[13,27],[14,27],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0064","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[14,29],[15,29],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 14/29, 15/29, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 14/29, 15/29, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235064,"parameters":{"n":7,"family":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[14,29],[15,29],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,4,5,6],[1,2,3]],\"n\":7,\"values\":[[0,1],[14,29],[15,29],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0065","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[15,31],[16,31],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 15/31, 16/31, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 15/31, 16/31, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235065,"parameters":{"n":7,"family":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[15,31],[16,31],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3],[4,5,6]],\"n\":7,\"values\":[[0,1],[15,31],[16,31],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0066","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[16,33],[17,33],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 16/33, 17/33, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 16/33, 17/33, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235066,"parameters":{"n":7,"family":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[16,33],[17,33],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3,5,6],[4]],\"n\":7,\"values\":[[0,1],[16,33],[17,33],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0067","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[17,35],[18,35],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 17/35, 18/35, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 17/35, 18/35, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235067,"parameters":{"n":7,"family":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[17,35],[18,35],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,4],[1,2,3,5,6]],\"n\":7,\"values\":[[0,1],[17,35],[18,35],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0068","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[18,37],[19,37],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 18/37, 19/37, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 18/37, 19/37, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235068,"parameters":{"n":7,"family":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[18,37],[19,37],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,5,6],[1,4]],\"n\":7,\"values\":[[0,1],[18,37],[19,37],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0069","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[19,39],[20,39],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 19/39, 20/39, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 19/39, 20/39, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235069,"parameters":{"n":7,"family":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[19,39],[20,39],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4],[2,3,5,6]],\"n\":7,\"values\":[[0,1],[19,39],[20,39],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0070","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[20,41],[21,41],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 20/41, 21/41, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 20/41, 21/41, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235070,"parameters":{"n":7,"family":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[20,41],[21,41],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,5,6],[2,4]],\"n\":7,\"values\":[[0,1],[20,41],[21,41],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0071","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[21,43],[22,43],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 21/43, 22/43, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 21/43, 22/43, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235071,"parameters":{"n":7,"family":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[21,43],[22,43],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4],[1,3,5,6]],\"n\":7,\"values\":[[0,1],[21,43],[22,43],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0072","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[22,45],[23,45],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 22/45, 23/45, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 22/45, 23/45, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235072,"parameters":{"n":7,"family":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[22,45],[23,45],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,5,6],[1,2,4]],\"n\":7,\"values\":[[0,1],[22,45],[23,45],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0073","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[23,47],[24,47],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 23/47, 24/47, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 23/47, 24/47, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235073,"parameters":{"n":7,"family":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[23,47],[24,47],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4],[3,5,6]],\"n\":7,\"values\":[[0,1],[23,47],[24,47],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0074","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[24,49],[25,49],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 24/49, 25/49, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 24/49, 25/49, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235074,"parameters":{"n":7,"family":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[24,49],[25,49],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,5,6],[3,4]],\"n\":7,\"values\":[[0,1],[24,49],[25,49],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0075","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-measure-additivity-audit；資料={\"n\":7,\"family\":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[25,51],[26,51],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,finite_countable_reduction] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 25/51, 26/51, 1], 是, [], 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 25/51, 26/51, 1], 是, [], 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-measure-additivity-audit","seed":202610235075,"parameters":{"n":7,"family":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[25,51],[26,51],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-measure-additivity-audit","semantic_template":"qf-mod23-measure-measure-additivity-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4],[1,2,5,6]],\"n\":7,\"values\":[[0,1],[25,51],[26,51],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0076","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[1,3],[2,3],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 1/3, 2/3, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0], [1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 1/3, 2/3, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235076,"parameters":{"n":7,"family":[[],[0],[1,2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[1,3],[2,3],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0],[1,2,3,4,5,6]],\"n\":7,\"values\":[[0,1],[1,3],[2,3],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0077","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[2,5],[3,5],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 2/5, 3/5, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1], [0, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 2/5, 3/5, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235077,"parameters":{"n":7,"family":[[],[1],[0,2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[2,5],[3,5],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,4,5,6],[1]],\"n\":7,\"values\":[[0,1],[2,5],[3,5],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0078","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[3,7],[4,7],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 3/7, 4/7, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1], [2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 3/7, 4/7, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235078,"parameters":{"n":7,"family":[[],[0,1],[2,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[3,7],[4,7],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1],[2,3,4,5,6]],\"n\":7,\"values\":[[0,1],[3,7],[4,7],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0079","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[4,9],[5,9],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 4/9, 5/9, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2], [0, 1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 4/9, 5/9, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235079,"parameters":{"n":7,"family":[[],[2],[0,1,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[4,9],[5,9],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,4,5,6],[2]],\"n\":7,\"values\":[[0,1],[4,9],[5,9],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0080","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[5,11],[6,11],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 5/11, 6/11, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2], [1, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 5/11, 6/11, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235080,"parameters":{"n":7,"family":[[],[0,2],[1,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[5,11],[6,11],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2],[1,3,4,5,6]],\"n\":7,\"values\":[[0,1],[5,11],[6,11],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0081","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[6,13],[7,13],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 6/13, 7/13, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2], [0, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 6/13, 7/13, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235081,"parameters":{"n":7,"family":[[],[1,2],[0,3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[6,13],[7,13],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4,5,6],[1,2]],\"n\":7,\"values\":[[0,1],[6,13],[7,13],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0082","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[7,15],[8,15],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 7/15, 8/15, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2], [3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 7/15, 8/15, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235082,"parameters":{"n":7,"family":[[],[0,1,2],[3,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[7,15],[8,15],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2],[3,4,5,6]],\"n\":7,\"values\":[[0,1],[7,15],[8,15],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0083","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[8,17],[9,17],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 8/17, 9/17, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [3], [0, 1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 8/17, 9/17, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235083,"parameters":{"n":7,"family":[[],[3],[0,1,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[8,17],[9,17],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4,5,6],[3]],\"n\":7,\"values\":[[0,1],[8,17],[9,17],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0084","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[9,19],[10,19],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 9/19, 10/19, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3], [1, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 9/19, 10/19, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235084,"parameters":{"n":7,"family":[[],[0,3],[1,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[9,19],[10,19],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3],[1,2,4,5,6]],\"n\":7,\"values\":[[0,1],[9,19],[10,19],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0085","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[10,21],[11,21],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 10/21, 11/21, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 3], [0, 2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 10/21, 11/21, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235085,"parameters":{"n":7,"family":[[],[1,3],[0,2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[10,21],[11,21],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4,5,6],[1,3]],\"n\":7,\"values\":[[0,1],[10,21],[11,21],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0086","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[11,23],[12,23],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 11/23, 12/23, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 3], [2, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 11/23, 12/23, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235086,"parameters":{"n":7,"family":[[],[0,1,3],[2,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[11,23],[12,23],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3],[2,4,5,6]],\"n\":7,\"values\":[[0,1],[11,23],[12,23],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0087","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[12,25],[13,25],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 12/25, 13/25, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 3], [0, 1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 12/25, 13/25, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235087,"parameters":{"n":7,"family":[[],[2,3],[0,1,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[12,25],[13,25],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4,5,6],[2,3]],\"n\":7,\"values\":[[0,1],[12,25],[13,25],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0088","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[13,27],[14,27],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 13/27, 14/27, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 3], [1, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 13/27, 14/27, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235088,"parameters":{"n":7,"family":[[],[0,2,3],[1,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[13,27],[14,27],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3],[1,4,5,6]],\"n\":7,\"values\":[[0,1],[13,27],[14,27],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0089","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[14,29],[15,29],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 14/29, 15/29, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 3], [0, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 14/29, 15/29, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235089,"parameters":{"n":7,"family":[[],[1,2,3],[0,4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[14,29],[15,29],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,4,5,6],[1,2,3]],\"n\":7,\"values\":[[0,1],[14,29],[15,29],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0090","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[15,31],[16,31],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 15/31, 16/31, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 3], [4, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 15/31, 16/31, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235090,"parameters":{"n":7,"family":[[],[0,1,2,3],[4,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[15,31],[16,31],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3],[4,5,6]],\"n\":7,\"values\":[[0,1],[15,31],[16,31],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0091","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[16,33],[17,33],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 16/33, 17/33, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [4], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 16/33, 17/33, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235091,"parameters":{"n":7,"family":[[],[4],[0,1,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[16,33],[17,33],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,3,5,6],[4]],\"n\":7,\"values\":[[0,1],[16,33],[17,33],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0092","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[17,35],[18,35],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 17/35, 18/35, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 4], [1, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 17/35, 18/35, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235092,"parameters":{"n":7,"family":[[],[0,4],[1,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[17,35],[18,35],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,4],[1,2,3,5,6]],\"n\":7,\"values\":[[0,1],[17,35],[18,35],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0093","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[18,37],[19,37],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 18/37, 19/37, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 4], [0, 2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 18/37, 19/37, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235093,"parameters":{"n":7,"family":[[],[1,4],[0,2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[18,37],[19,37],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,3,5,6],[1,4]],\"n\":7,\"values\":[[0,1],[18,37],[19,37],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0094","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[19,39],[20,39],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 19/39, 20/39, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 4], [2, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 19/39, 20/39, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235094,"parameters":{"n":7,"family":[[],[0,1,4],[2,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[19,39],[20,39],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,4],[2,3,5,6]],\"n\":7,\"values\":[[0,1],[19,39],[20,39],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0095","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[20,41],[21,41],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 20/41, 21/41, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [2, 4], [0, 1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 20/41, 21/41, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235095,"parameters":{"n":7,"family":[[],[2,4],[0,1,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[20,41],[21,41],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,3,5,6],[2,4]],\"n\":7,\"values\":[[0,1],[20,41],[21,41],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0096","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[21,43],[22,43],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 21/43, 22/43, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 2, 4], [1, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 21/43, 22/43, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235096,"parameters":{"n":7,"family":[[],[0,2,4],[1,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[21,43],[22,43],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,2,4],[1,3,5,6]],\"n\":7,\"values\":[[0,1],[21,43],[22,43],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0097","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[22,45],[23,45],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 22/45, 23/45, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [1, 2, 4], [0, 3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 22/45, 23/45, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235097,"parameters":{"n":7,"family":[[],[1,2,4],[0,3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[22,45],[23,45],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,5,6],[1,2,4]],\"n\":7,\"values\":[[0,1],[22,45],[23,45],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0098","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[23,47],[24,47],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 23/47, 24/47, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 1, 2, 4], [3, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 23/47, 24/47, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235098,"parameters":{"n":7,"family":[[],[0,1,2,4],[3,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[23,47],[24,47],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,4],[3,5,6]],\"n\":7,\"values\":[[0,1],[23,47],[24,47],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0099","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[24,49],[25,49],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 24/49, 25/49, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [3, 4], [0, 1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 24/49, 25/49, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235099,"parameters":{"n":7,"family":[[],[3,4],[0,1,2,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[24,49],[25,49],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,1,2,5,6],[3,4]],\"n\":7,\"values\":[[0,1],[24,49],[25,49],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261023-r05-sigma-algebra-measure-space-0100","batch_id":"batch-20261013-advance-20261023-r05-sigma-algebra-measure-space-foundations","language":"zh-Hant","source_mko_ids":["mko-sigma-algebra-measure-space"],"title_zh":"有限測度空間","stem_zh":"完整有限載體與canonical集合族。操作=measure-probability-measure-audit；資料={\"n\":7,\"family\":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],\"values\":[[0,1],[25,51],[26,51],[1,1]]}。請依 [n,family,values,empty_zero,bad_disjoint_pairs,total,finite_countable_reduction,probability_measure] 欄序回答。","answer":{"kind":"expression","value":"(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 25/51, 26/51, 1], 是, [], 1, 是, 是)","explanation_zh":"現代橋梁核對=(7, [[], [0, 3, 4], [1, 2, 5, 6], [0, 1, 2, 3, 4, 5, 6]], [0, 25/51, 26/51, 1], 是, [], 1, 是, 是)；依完整明示資料重算；完整明示的有限／精確切片不自動升格為一般無限結論；可數語義只由指定有限載體歸約；不外推任意無限測度空間。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限測度空間"]},"variant":{"family_id":"qf-mod23-measure-probability-measure-audit","seed":202610235100,"parameters":{"n":7,"family":[[],[0,3,4],[1,2,5,6],[0,1,2,3,4,5,6]],"values":[[0,1],[25,51],[26,51],[1,1]],"domain":"Complete_finite_measure_space","operation":"measure-probability-measure-audit","semantic_template":"qf-mod23-measure-probability-measure-audit/{\"family\":[[],[0,1,2,3,4,5,6],[0,3,4],[1,2,5,6]],\"n\":7,\"values\":[[0,1],[25,51],[26,51],[1,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov／可微聲明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}