Abstract: In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of theα-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.

Key words:  Borel-Cantelli lemma, strong mixing, a-mixing, strong law of large numbers