Anděl, Jiří; Dupač, Václav An extension of the Borel lemma. (English) Zbl 0678.60030 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 Cited in 2 ReviewsCited in 6 Documents MSC: 60F15 Strong limit theorems 60F20 Zero-one laws Keywords:Borel-Cantelli lemma PDF BibTeX XML Cite \textit{J. Anděl} and \textit{V. Dupač}, Commentat. Math. Univ. Carol. 30, No. 2, 403--404 (1989; Zbl 0678.60030) OpenURL