2017•arXiv (Cornell University)Open access

On the Strong Law of Large Numbers for Sequences of Pairwise Independent\n Random Variables

V. M. Korchevsky

Abstract

We establish new sufficient conditions for the applicability of the strong\nlaw of large numbers (SLLN) for sequences of pairwise independent\nnon-identically distributed random variables. These results generalize\nEtemadi's extension of Kolmogorov's SLLN for identically distributed random\nvariables. Some of the obtained results hold with an arbitrary norming sequence\nin place of the classical normalization.\n

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Key concepts: Independent and identically distributed random variables, Pairwise comparison, Pairwise independence, Law of large numbers, Mathematics, Normalization (sociology), Random variable, Sequence (biology)