{
  "$schema":"../../../schemas/mko-v0.4.schema.json","schema_version":"mko-v0.4","id":"mko-event","semantic_family_id":"sf-event","type":"definition","version":"0.10.0","language":"zh-Hant",
  "titles":{"zh-Hant":"事件","en":"Event"},
  "summary":{"zh-Hant":"事件描述隨機試驗中關心的一組可能結果。"},
  "statement":{"zh-Hant":"本條目的有限初等模型明示採完整事件族 F=P(S)，因此事件 E 可取 S 的任一子集合；一般指定為 (S,F) 的模型不論 S 有限或無限，都要求事件 E 屬於 F。試驗結果屬於 E 時稱事件 E 發生。"},
  "formula":{"tex":"E\\subseteq S","mathml":"<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>E</mi><mo>⊆</mo><mi>S</mi></mrow></math>","semantic_ast":{"type":"set_subset","subset":{"type":"symbol","name":"E","glyph":"E"},"superset":{"type":"symbol","name":"S","glyph":"S"}},"compiler":{"id":"ocme-formula-core","version":"0.4.0","source_sha256":"bdc7f74c71488751864a93bb57307ebc5057cf96bf7ec12f3878879c2c8c81ef"}},
  "assumptions":[{"id":"a1","zh-Hant":"隨機試驗與樣本空間 S 已明確指定。"},{"id":"a2","zh-Hant":"有限初等題明示採 F=P(S)；其他模型已明示事件族 F，且事件必須屬於 F。"}],
  "symbols":[{"token":"E","role":"event","role_zh":"事件集合","scope":"definition"},{"token":"S","role":"sample_space","role_zh":"樣本空間","scope":"definition"},{"token":"⊆","role":"subset_relation","role_zh":"事件包含於樣本空間","scope":"definition"}],
  "dependencies":[{"id":"mko-sample-space","title_zh":"樣本空間","reason_zh":"事件必須相對一個明示的結果論域定義。"},{"id":"mko-subset","title_zh":"子集合","reason_zh":"初等事件以樣本空間的子集合表示。"}],
  "explanation":{"paragraphs_zh":["單一結果是樣本空間的一個元素；事件通常是一個結果集合，兩者不可混同。","空事件不含任何結果，必然事件包含整個樣本空間；這些名稱不等於本條目已為它們指定機率值。","只有明示採完整冪集 F=P(S) 時，每個子集合才都可作事件；一般模型即使 S 有限，也仍須檢查 E∈F。"],"common_misconception_zh":"常見誤解是把事件當成單一結果、在未指定樣本空間或事件族時列事件，或認為樣本空間有限就自動讓所有子集合可測。"},
  "proofs":[],"computational_companions":[],
  "verification":{"computational_status":"not_evaluated_no_computational_claim","warning_zh":"有限集合檢查只驗證具體包含關係，不建立一般可測性或機率公理。","evidence_refs":[],"producers":[{"id":"lean-mathlib","adapter":"formal_system","config_path":"formal/lean/lakefile.toml","status":"configured"}]},
  "formalization":{"status":"not_formalized","target_systems":["Lean 4","Mathlib"],"next_obligation_zh":"分開形式化 F=P(S) 的有限初等模型與一般 E∈F／MeasurableSet 邊界，並綁定版本與 axiom receipt。"},
  "provenance":{"origin":"ocme_local_ai_materialization_candidate","note_zh":"依 research/atlas-event.md 整理；待人工審查。","content_license":"CC-BY-SA-4.0","code_license":"MIT","created_at":"2026-09-18"}
}