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

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We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent, nonidentically 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.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. M. Korchevsky

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  1. V. M. Korchevsky
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Correspondence to V. M. Korchevsky.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 120–133.

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Korchevsky, V.M. On the Strong Law of Large Numbers for Sequences of Pairwise Independent Random Variables. J Math Sci 244, 805–810 (2020). https://doi.org/10.1007/s10958-020-04654-y

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  • DOI: https://doi.org/10.1007/s10958-020-04654-y

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