Geodesic
On an infinite-dimensional version of S.\,N.~Bernstein's inequalities
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 106-107

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Probability inequalities for sums of bounded independent random vectors in a Hilbert space are obtained. Reduction to one-ditnensieeal case yields a considerable simplification of the proofs. 
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     author = {V. V. Yurinskii},
     title = {On an infinite-dimensional version of {S.\,N.~Bernstein's} inequalities},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a7/}
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V. V. Yurinskii. On an infinite-dimensional version of S.\,N.~Bernstein's inequalities. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 106-107. http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a7/