Geodesic
Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 327-341 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the approach of Etemadi for the strong law of large numbers [Z.Wahrsch. Verw. Gebiete, 55 (1981), pp. 119–122] and its elaboration by Csörgő, Tandori, and Totik [Acta Math.Hungar., 42 (1983), pp. 319–330], we give weaker conditions under which the strong law of large numbers still holds, namely for pairwise uncorrelated (and also for “quasi-uncorrelated”) random variables. We focus, in particular, on random variables which are not identically distributed. Our approach leads to another simple proof of the classical strong law of large numbers.
Keywords: strong law of large numbers, Kolmogorov condition, Etemadi theorem, pairwise uncorrelated random variables, quasi-uncorrelated random variables. 
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M. Janisch. Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 327-341. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a5/

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