Talk:Kolmogorov's zero-one law

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[edit] ??

There is a minor sloppyness in language. The term \sum_{k=1}^\infty X_k is the limit of the series \big(\sum_{k=1}^N X_k\big)_{N=1}^\infty.

That's not a series; that's a sequence! Michael Hardy 00:36, 1 Nov 2004 (UTC)

The later converges or not, the prior exists or not.

What does it mean for a sum of random variables not to exist? I think you've misunderstood the point.

Don't know how to correct this without an overhead of explanation.

Btw., what are the exact requirements on X_k^{} for the series to converge at all? Certainly \operatorname E (X_k) = 0 is needed, but not sufficient. I even believe the convergences of the series would be equivalent to \operatorname P\{X_k = 0\} = 1.

No on both accounts. See eg. the central limit theorem.
ouch, now I see where I was wrong: in many theorems the random variables have to be identically distributed, not so here. 217.230.28.82 12:16, 31 Oct 2004 (UTC)