An extension of the Borel lemma. (English) Zbl 0678.60030

Anděl, Jiří; Dupač, Václav

Commentat. Math. Univ. Carol. 30, No. 2, 403-404 (1989).

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