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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
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