Geodesic
A remark on the strong law of large numbers
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 829-831
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In the paper, necessary and sufficient conditions are obtained for the strong law of large numbers in the case of normalization of sums of independent random variables by an arbitrary non-decreasing sequence of real numbers $\{b_n\}$, $b_n\uparrow\infty$. 
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     author = {N. A. Volodin and S. V. Nagaev},
     title = {A~remark on the strong law of large numbers},
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     year = {1977},
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N. A. Volodin; S. V. Nagaev. A remark on the strong law of large numbers. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 4, pp. 829-831. http://geodesic.mathdoc.fr/item/TVP_1977_22_4_a12/