Geodesic
On the distribution of sums of independent Banach-space-valued random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 630-637

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Probabilistic inequalities of [2] are generalized for the case of Banach-space-valued random variables with the help of the method due to V. V. Yurinski\u i [12]. As a consequence, sufficient conditions for the strong law of large numbers are given. The results obtained are compared with known ones in this direction. 
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     author = {I. F. Pinelis},
     title = {On the distribution of sums of independent {Banach-space-valued} random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {630--637},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a13/}
}
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I. F. Pinelis. On the distribution of sums of independent Banach-space-valued random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 630-637. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a13/