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Keywords:
Borel-Cantelli Lemma; Stirling numbers
Borel-Cantelli Lemma; Stirling numbers
Summary:
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.
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