# 可測函數密度：逆像集合律、常值映射與來源sigma細化基礎 · 脈衝 R05

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261013-advance-20261025-r05-measurable-function-foundations · 2026-10-13 · 100 題



## 1. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,0,0,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 0, 0, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)

收束波核對=([0, 0, 0, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0001/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 2. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,0,0,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 0, 0, 0], [1, 2], [0, 3], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([1, 0, 0, 0], [1, 2], [0, 3], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0002/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 3. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,0,0,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 0, 0, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([2, 0, 0, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0003/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 4. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,0,0,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 0, 0, 0], [0, 3], [1, 2], [0, 1, 2, 3], [], [], 是)

收束波核對=([3, 0, 0, 0], [0, 3], [1, 2], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0004/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 5. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,1,0,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 1, 0, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)

收束波核對=([0, 1, 0, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0005/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 6. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,1,0,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 1, 0, 0], [1, 2], [0, 3], [0, 1], [2, 3], [2, 3], 是)

收束波核對=([1, 1, 0, 0], [1, 2], [0, 3], [0, 1], [2, 3], [2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0006/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 7. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,1,0,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 1, 0, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([2, 1, 0, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0007/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 8. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,1,0,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 1, 0, 0], [0, 3], [1, 2], [0, 2, 3], [1], [1], 是)

收束波核對=([3, 1, 0, 0], [0, 3], [1, 2], [0, 2, 3], [1], [1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0008/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 9. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,2,0,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 2, 0, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)

收束波核對=([0, 2, 0, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0009/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 10. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,2,0,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 2, 0, 0], [1, 2], [0, 3], [0, 1], [2, 3], [2, 3], 是)

收束波核對=([1, 2, 0, 0], [1, 2], [0, 3], [0, 1], [2, 3], [2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0010/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 11. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,2,0,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 2, 0, 0], [2, 3], [0, 1], [0, 1], [2, 3], [2, 3], 是)

收束波核對=([2, 2, 0, 0], [2, 3], [0, 1], [0, 1], [2, 3], [2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0011/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 12. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,2,0,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 2, 0, 0], [0, 3], [1, 2], [0, 2, 3], [1], [1], 是)

收束波核對=([3, 2, 0, 0], [0, 3], [1, 2], [0, 2, 3], [1], [1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0012/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 13. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,3,0,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 3, 0, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)

收束波核對=([0, 3, 0, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0013/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 14. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,3,0,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 3, 0, 0], [1, 2], [0, 3], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([1, 3, 0, 0], [1, 2], [0, 3], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0014/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 15. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,3,0,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 3, 0, 0], [2, 3], [0, 1], [0, 1], [2, 3], [2, 3], 是)

收束波核對=([2, 3, 0, 0], [2, 3], [0, 1], [0, 1], [2, 3], [2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0015/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 16. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,3,0,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 3, 0, 0], [0, 3], [1, 2], [0, 1, 2, 3], [], [], 是)

收束波核對=([3, 3, 0, 0], [0, 3], [1, 2], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0016/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 17. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,0,1,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 0, 1, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)

收束波核對=([0, 0, 1, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0017/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 18. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,0,1,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 0, 1, 0], [1, 2], [0, 3], [0, 2], [1, 3], [1, 3], 是)

收束波核對=([1, 0, 1, 0], [1, 2], [0, 3], [0, 2], [1, 3], [1, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0018/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 19. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,0,1,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 0, 1, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([2, 0, 1, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0019/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 20. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,0,1,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 0, 1, 0], [0, 3], [1, 2], [0, 1, 3], [2], [2], 是)

收束波核對=([3, 0, 1, 0], [0, 3], [1, 2], [0, 1, 3], [2], [2], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0020/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 21. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,1,1,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 1, 1, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)

收束波核對=([0, 1, 1, 0], [0, 1], [2, 3], [0, 1, 2, 3], [], [], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0021/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 22. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[1,1,1,0],"event":[1,2]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([1, 1, 1, 0], [1, 2], [0, 3], [0, 1, 2], [3], [3], 是)

收束波核對=([1, 1, 1, 0], [1, 2], [0, 3], [0, 1, 2], [3], [3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0022/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 23. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[2,1,1,0],"event":[2,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([2, 1, 1, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)

收束波核對=([2, 1, 1, 0], [2, 3], [0, 1], [0], [1, 2, 3], [1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0023/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 24. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[3,1,1,0],"event":[0,3]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([3, 1, 1, 0], [0, 3], [1, 2], [0, 3], [1, 2], [1, 2], 是)

收束波核對=([3, 1, 1, 0], [0, 3], [1, 2], [0, 3], [1, 2], [1, 2], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0024/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 25. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-complement-law；資料={"source_n":4,"target_n":4,"mapping":[0,2,1,0],"event":[0,1]}。請依 [mapping,event,target_complement,preimage,source_complement,preimage_of_complement,equal] 欄序回答。

查看答案與解釋([0, 2, 1, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)

收束波核對=([0, 2, 1, 0], [0, 1], [2, 3], [0, 2, 3], [1], [1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0025/)

可測函數 · qf-mod25-measdeep-preimage-complement-law · candidate





## 26. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,0,0,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 0, 0, 0], [0], [1, 2], [0, 1, 2], [0, 1, 2, 3], [], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 0, 0, 0], [0], [1, 2], [0, 1, 2], [0, 1, 2, 3], [], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0026/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 27. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,0,0,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 0, 0, 0], [1], [2, 3], [1, 2, 3], [0], [], [0], [0], 是)

收束波核對=([1, 0, 0, 0], [1], [2, 3], [1, 2, 3], [0], [], [0], [0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0027/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 28. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,0,0,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 0, 0, 0], [2], [0, 3], [0, 2, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([2, 0, 0, 0], [2], [0, 3], [0, 2, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0028/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 29. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,0,0,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 0, 0, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([3, 0, 0, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0029/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 30. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,1,0,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 1, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [1], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 1, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [1], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0030/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 31. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,1,0,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 1, 0, 0], [1], [2, 3], [1, 2, 3], [0, 1], [], [0, 1], [0, 1], 是)

收束波核對=([1, 1, 0, 0], [1], [2, 3], [1, 2, 3], [0, 1], [], [0, 1], [0, 1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0031/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 32. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,1,0,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 1, 0, 0], [2], [0, 3], [0, 2, 3], [0], [2, 3], [0, 2, 3], [0, 2, 3], 是)

收束波核對=([2, 1, 0, 0], [2], [0, 3], [0, 2, 3], [0], [2, 3], [0, 2, 3], [0, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0032/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 33. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,1,0,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 1, 0, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([3, 1, 0, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0033/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 34. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,2,0,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 2, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [1], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 2, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [1], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0034/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 35. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,2,0,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 2, 0, 0], [1], [2, 3], [1, 2, 3], [0], [1], [0, 1], [0, 1], 是)

收束波核對=([1, 2, 0, 0], [1], [2, 3], [1, 2, 3], [0], [1], [0, 1], [0, 1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0035/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 36. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,2,0,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 2, 0, 0], [2], [0, 3], [0, 2, 3], [0, 1], [2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([2, 2, 0, 0], [2], [0, 3], [0, 2, 3], [0, 1], [2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0036/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 37. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,2,0,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 2, 0, 0], [3], [0, 1], [0, 1, 3], [0], [2, 3], [0, 2, 3], [0, 2, 3], 是)

收束波核對=([3, 2, 0, 0], [3], [0, 1], [0, 1, 3], [0], [2, 3], [0, 2, 3], [0, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0037/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 38. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,3,0,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 3, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [], [0, 2, 3], [0, 2, 3], 是)

收束波核對=([0, 3, 0, 0], [0], [1, 2], [0, 1, 2], [0, 2, 3], [], [0, 2, 3], [0, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0038/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 39. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,3,0,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 3, 0, 0], [1], [2, 3], [1, 2, 3], [0], [1], [0, 1], [0, 1], 是)

收束波核對=([1, 3, 0, 0], [1], [2, 3], [1, 2, 3], [0], [1], [0, 1], [0, 1], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0039/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 40. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,3,0,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 3, 0, 0], [2], [0, 3], [0, 2, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([2, 3, 0, 0], [2], [0, 3], [0, 2, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0040/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 41. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,3,0,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 3, 0, 0], [3], [0, 1], [0, 1, 3], [0, 1], [2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([3, 3, 0, 0], [3], [0, 1], [0, 1, 3], [0, 1], [2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0041/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 42. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,0,1,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 0, 1, 0], [0], [1, 2], [0, 1, 2], [0, 1, 3], [2], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 0, 1, 0], [0], [1, 2], [0, 1, 2], [0, 1, 3], [2], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0042/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 43. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,0,1,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 0, 1, 0], [1], [2, 3], [1, 2, 3], [0, 2], [], [0, 2], [0, 2], 是)

收束波核對=([1, 0, 1, 0], [1], [2, 3], [1, 2, 3], [0, 2], [], [0, 2], [0, 2], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0043/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 44. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,0,1,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 0, 1, 0], [2], [0, 3], [0, 2, 3], [0], [1, 3], [0, 1, 3], [0, 1, 3], 是)

收束波核對=([2, 0, 1, 0], [2], [0, 3], [0, 2, 3], [0], [1, 3], [0, 1, 3], [0, 1, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0044/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 45. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,0,1,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 0, 1, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([3, 0, 1, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0045/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 46. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,1,1,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 1, 1, 0], [0], [1, 2], [0, 1, 2], [0, 3], [1, 2], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 1, 1, 0], [0], [1, 2], [0, 1, 2], [0, 3], [1, 2], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0046/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 47. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[1,1,1,0],"left_event":[1],"right_event":[2,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([1, 1, 1, 0], [1], [2, 3], [1, 2, 3], [0, 1, 2], [], [0, 1, 2], [0, 1, 2], 是)

收束波核對=([1, 1, 1, 0], [1], [2, 3], [1, 2, 3], [0, 1, 2], [], [0, 1, 2], [0, 1, 2], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0047/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 48. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[2,1,1,0],"left_event":[2],"right_event":[0,3]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([2, 1, 1, 0], [2], [0, 3], [0, 2, 3], [0], [3], [0, 3], [0, 3], 是)

收束波核對=([2, 1, 1, 0], [2], [0, 3], [0, 2, 3], [0], [3], [0, 3], [0, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0048/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 49. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[3,1,1,0],"left_event":[3],"right_event":[0,1]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([3, 1, 1, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([3, 1, 1, 0], [3], [0, 1], [0, 1, 3], [0], [1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0049/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 50. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-preimage-union-law；資料={"source_n":4,"target_n":4,"mapping":[0,2,1,0],"left_event":[0],"right_event":[1,2]}。請依 [mapping,left,right,union,left_preimage,right_preimage,union_preimage,preimage_union,equal] 欄序回答。

查看答案與解釋([0, 2, 1, 0], [0], [1, 2], [0, 1, 2], [0, 3], [1, 2], [0, 1, 2, 3], [0, 1, 2, 3], 是)

收束波核對=([0, 2, 1, 0], [0], [1, 2], [0, 1, 2], [0, 3], [1, 2], [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0050/)

可測函數 · qf-mod25-measdeep-preimage-union-law · candidate





## 51. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0051/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 52. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0052/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 53. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0053/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 54. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0054/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 55. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0055/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 56. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0056/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 57. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0057/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 58. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0058/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 59. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0059/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 60. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0060/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 61. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0061/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 62. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0062/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 63. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0063/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 64. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0064/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 65. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0065/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 66. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0066/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 67. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0067/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 68. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0068/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 69. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0069/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 70. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0070/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 71. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0071/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 72. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":1}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 1, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0072/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 73. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":2}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 2, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0073/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 74. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":3}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 3, [3, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [], 是], [[0, 1, 2], [], 是], [[3], [0, 1, 2, 3], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0074/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 75. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-constant-map-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"value":0}。請依 [source_n,target_n,value,mapping,preimage_rows,measurable] 欄序回答。

查看答案與解釋(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=(4, 4, 0, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0075/)

可測函數 · qf-mod25-measdeep-constant-map-audit · candidate





## 76. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,0,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 0, 0, 0], 是, [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 0, 0, 0], 是, [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0076/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 77. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,0,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [0], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 否], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [0], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [0], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [0], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 否], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [0], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [0], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0077/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 78. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,0,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0078/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 79. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,0,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [1, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 0, 0, 0], 是, [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [1, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0079/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 80. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,1,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 1, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 1, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0080/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 81. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,1,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [0, 1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0, 1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [0, 1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0, 1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0081/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 82. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,1,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0082/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 83. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,1,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 1, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0083/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 84. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,2,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 2, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 2, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0084/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 85. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,2,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 否], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [1, 2, 3], 否], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 否], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [1, 2, 3], 否], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0085/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 86. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,2,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0, 1], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [0, 1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0, 1], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [0, 1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0086/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 87. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,2,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [1], 否], [[0, 2], [1, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 2, 3], 否], [[1, 3], [0], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 2, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [1], 否], [[0, 2], [1, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 2, 3], 否], [[1, 3], [0], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0087/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 88. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,3,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 3, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [], 是], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 3, 0, 0], 是, [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [], 是], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0088/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 89. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,3,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [0], 否], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [0], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [0], 否], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [0], 否], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 否], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [1, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0089/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 90. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,3,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [0], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [0], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0090/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 91. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,3,0,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 否], [[3], [0, 1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 是], [[3], [0, 1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 3, 0, 0], 是, [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [], 是], [[0, 2], [2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 否], [[3], [0, 1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 是], [[3], [0, 1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0091/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 92. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,0,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 0, 1, 0], 是, [[[], [], 是], [[0], [0, 1, 3], 否], [[1], [2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 否], [[1, 3], [2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 1, 3], 是], [[1], [2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 0, 1, 0], 是, [[[], [], 是], [[0], [0, 1, 3], 否], [[1], [2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 否], [[1, 3], [2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 1, 3], 是], [[1], [2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0092/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 93. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,0,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 否], [[1], [0, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 否], [[1, 3], [0, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 否], [[1, 2, 3], [0, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [0, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 否], [[1], [0, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 否], [[1, 2], [0, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 否], [[1, 3], [0, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 否], [[1, 2, 3], [0, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [0, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0093/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 94. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,0,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 3], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 3], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0094/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 95. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,0,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 否], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 1, 3], 否], [[1, 3], [0, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 0, 1, 0], 是, [[[], [], 是], [[0], [1, 3], 否], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 1, 3], 否], [[1, 3], [0, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0095/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 96. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,1,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 1, 1, 0], 是, [[[], [], 是], [[0], [0, 3], 否], [[1], [1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 3], 是], [[1], [1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 1, 1, 0], 是, [[[], [], 是], [[0], [0, 3], 否], [[1], [1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 3], 是], [[1], [1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0096/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 97. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,1,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([1, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [0, 1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [0, 1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [0, 1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([1, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [0, 1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [0, 1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [0, 1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0097/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 98. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,1,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([2, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([2, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [0], 是], [[0, 2], [0, 3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0098/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 99. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,1,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([3, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 3], 否], [[1, 3], [0, 1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([3, 1, 1, 0], 是, [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [], 是], [[0, 2], [3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [1, 2, 3], 否], [[3], [0], 否], [[0, 3], [0, 3], 否], [[1, 3], [0, 1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0099/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate





## 100. 可測函數密度

完整有限sigma代數與總映射。操作=measdeep-source-sigma-refinement-audit；資料={"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"refined_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,2,1,0]}。請依 [mapping,is_refinement,before_rows,before_measurable,after_rows,after_measurable] 欄序回答。

查看答案與解釋([0, 2, 1, 0], 是, [[[], [], 是], [[0], [0, 3], 否], [[1], [2], 是], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 3], 是], [[1], [2], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)

收束波核對=([0, 2, 1, 0], 是, [[[], [], 是], [[0], [0, 3], 否], [[1], [2], 是], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, [[[], [], 是], [[0], [0, 3], 是], [[1], [2], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 是], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；集合律一律由逆像核對；不推出連續可積保測或無限空間結論。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261013-advance-20261025-r05-measurable-function-0100/)

可測函數 · qf-mod25-measdeep-source-sigma-refinement-audit · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261025-r05-measurable-function-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261025-r05-measurable-function-foundations/validation-report.json)