Criteria of regularity at the end of a tree
On the Borel-Cantelli Lemma and moments
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., , Statist. Probab. Lett. (2004), no. 3, 233–239.
On sums involving binomial coefficients.
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