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This question already has an answer here:

Here is another corollary of the theorem: Kolmogorov zero-one law given in my textbook (Probability path). How can I apply the said theorem given that if $X_n$ are independent random variables, $[\sum_nX_n \mbox{ converges}]$ has probability 0 or 1. thanks :-)

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marked as duplicate by Did probability-theory Nov 12 '14 at 17:56

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Hint: show that this event is in the tail $\sigma$-field.

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  • $\begingroup$ Is it taking the lim sup of Xn? $\endgroup$ – mogs Sep 29 '14 at 6:54

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