Kolmogorov's strong law of large numbers holds for pairwise uncorrelated random variables

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.