→ sato186 :你的定義怪怪的... 10/09 23:48
→ gozule :我是參考wiki寫σ-algebra的定義 10/10 01:22
※ 編輯: gozule 來自: 114.136.149.188 (10/10 01:26)
Ω be some set, F is subset of P(Ω) ( power set of Ω)
F is called σ-algebra if it satisfies:
1. F is non-empty
2. If A is in F, then ~A (~A = Ω\A) is also in F.
3 If A_i in F, i=1,2,..., then ∪(A_i) in F.
以上是σ-algebra的定義，而我在書上看到範例如下：
C={A, B} is family of subset of Ω
A∩B≠Φ
F1 = {Φ, A∩B, ~A∩B, A∩~B, ~A∩~B, Ω} is σ-algebra
我的問題是在F1當中，~(A∩B) = ~A∪~B 並不存在F1，即不滿足條件2
為何F1為σ-algebra?
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