Geodesic
On random series in a Banach space
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 491-505 
V. V. Buldygin. On random series in a Banach space. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 491-505. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a4/
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     author = {V. V. Buldygin},
     title = {On random series in {a~Banach} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {491--505},
     year = {1973},
     volume = {18},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions are obtained for a series of independent random variables in a Banach space to converge almost surely.