Question: Consider any events (independent or not) A n ,n ¥ 1, and suppose that P(A n ) < . Then P(lim sup n A n

Consider any events (independent or not) A_n,n ‰¥ 1, and suppose that

P(A_n) < ˆž. Then P(lim sup_n†’ˆžA_n) = 0. This is so by Theorem 3 in this chapter (see also Theorem 4(i)). Regarding the converse of this statement, we have that, if P(lim sup_n†’ˆž.A_n) = 0 and the events A_n,n ‰¥ 1, are independent, then

Justify this assertion.

00 n%=D1

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