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On the Strong Law of Large Numbers for Sequences of Pairwise Independent Random Variables (1701.02234v1)
Published 4 Jan 2017 in math.PR
Abstract: We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent non-identically distributed random variables. These results generalize Etemadi's extension of Kolmogorov's SLLN for identically distributed random variables. Some of the obtained results hold with an arbitrary norming sequence in place of the classical normalization.