# Talk:Kolmogorov's zero–one law

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## ??

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)

How about a rigorous definition for a tail event or tail sigma algebra? —Preceding unsigned comment added by 71.207.219.120 (talk) 07:48, 23 April 2009 (UTC)

The reason why this doesn't contradict the theorem is because the theorem should only be stated for events belonging to ${\mathcal {F}}$ .
Another issue is that you define a tail event as being one that is independent of all finite subsets of the $X_{i}$ , but this itself follows from the hypothesis that the $X_{i}$ are independent. In fact, under the article's definition of 'tail event', surely we don't even need to assume that the $X_{i}$ are independent for the result to be true (provided it's only stated for events in ${\mathcal {F}}$ )? —Preceding unsigned comment added by 92.15.133.253 (talk) 10:38, 6 August 2010 (UTC)