Theory of Probability &Its Applications, Volume 66, Issue 2, Page 263-275, January 2021.
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 Csörgö, 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.

中文翻译：

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Kolmogorov 的强数定律适用于成对不相关的随机变量

Theory of Probability & Its Applications，第 66 卷，第 2 期，第 263-275 页，2021 年 1 月。
使用 Etemadi 的方法求解强数定律 [Z. 瓦尔施。版本。Gebiete, 55 (1981), pp. 119--122] 及其由 Csörgö、Tandori 和 Totik [Acta Math. Hungar., 42 (1983), pp. 319--330]，我们给出了强数定律仍然成立的较弱条件，即成对不相关（以及“准不相关”）随机变量。我们特别关注非同分布的随机变量。我们的方法导致了经典强数定律的另一个简单证明。