Geodesic
On the strong law of large numbers
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 637-641

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Sufficient conditions for the strong law of large numbers are obtained in terms of sums of moments' products. The proof is based on the theorem of [2]. 
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S. V. Nagaev; N. A. Volodin. On the strong law of large numbers. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 637-641. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a13/