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An extension of the Borel lemma. (English) Zbl 0678.60030
Let $$A_ n$$, $$n\geq 1$$, be independent events, and let $$B_ n$$, $$n\geq 1$$, be events such that $$\lim P(B_ n| A_ n)=1$$. The purpose of this paper is to show that $P(\limsup A_ nB_ n)=1\text{ whenever }\sum^{\infty}_{n=1} P(A_ nB_ n)=\infty.$
Reviewer: A.Spătaru

##### MSC:
 60F15 Strong limit theorems 60F20 Zero-one laws
##### Keywords:
Borel-Cantelli lemma