→ FANggot :例子講的似乎是 A is not closed with respect to 04/02 14:19
→ FANggot :countable union. 04/02 14:20
推 mathblue :σ-algebra是coutable union之後都要原空間裡 04/02 15:38
If X is an infinite set, then
A = { E 屬於 X | E is cofinite } is an algebra but not σ-algebra on X
舉例:
∵ Any infinite set contains a countable infinite set.
Now, X is an infinite set, we can choose a countable infinite
subset A = { x_1, x_2, ... ...}
x_1 屬於 X , x_2 屬於 X－{ x_1} ,
x_3屬於 X－{ x_1, x_2},...以此類推...
Let E = { x_2,x_4,....} = {x_2n | n=1,2,...}
A_n = { x_2n}, n = 1,2,...
∞ _
But ∪ A_n = E 不屬於 A (∵ E is not finite 且 E is not finite)
n=1
看不懂黃色這個例子...可不可以講解一下..謝謝...^^
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※ 編輯: ericakk 來自: 58.114.225.200 (04/02 13:23)
※ 編輯: ericakk 來自: 58.114.225.200 (04/02 13:23)