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Mathematics版 - Kolmogrove 0-1 law question
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进入Mathematics版参与讨论
1 (共1页)
a***n
发帖数: 40
1
By Kolmogrove's 0-1 law, P(sigema |Xn| < infinitey) = 0 or 1.
Can we conclude that the infinite sum of |Xn| either converges almost surely,
or diverges almost surely?
Thank you.
H****h
发帖数: 1037
2
Yes.

,

【在 a***n 的大作中提到】
: By Kolmogrove's 0-1 law, P(sigema |Xn| < infinitey) = 0 or 1.
: Can we conclude that the infinite sum of |Xn| either converges almost surely,
: or diverges almost surely?
: Thank you.

c*******n
发帖数: 718
3
No, only when Xn is independent

,

【在 a***n 的大作中提到】
: By Kolmogrove's 0-1 law, P(sigema |Xn| < infinitey) = 0 or 1.
: Can we conclude that the infinite sum of |Xn| either converges almost surely,
: or diverges almost surely?
: Thank you.

H****h
发帖数: 1037
4
Yes.

,

【在 a***n 的大作中提到】
: By Kolmogrove's 0-1 law, P(sigema |Xn| < infinitey) = 0 or 1.
: Can we conclude that the infinite sum of |Xn| either converges almost surely,
: or diverges almost surely?
: Thank you.

1 (共1页)
进入Mathematics版参与讨论
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