Geodesic
On the Borel-Cantelli Lemma and moments
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 669-679.

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We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., {\it A generalization of the Borel-Cantelli Lemma\/}, Statist. Probab. Lett. {\bf 67} (2004), no. 3, 233--239.
Classification : 05A18, 60A10, 60F15
Keywords: Borel-Cantelli Lemma; Stirling numbers 
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Amghibech, S. On the Borel-Cantelli Lemma and moments. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 669-679. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a11/