## 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