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February, 1981 Inequalities for $B$-Valued Random Vectors with Applications to the Strong Law of Large Numbers
Alejandro De Acosta
Ann. Probab. 9(1): 157-161 (February, 1981). DOI: 10.1214/aop/1176994517

Abstract

Analogues of the Marcinkiewicz-Zygmund and Rosenthal inequalities for Banach space valued random vectors are proved. As an application some results on the strong law of large numbers are obtained. It is proved that the Marcinkiewicz SLLN holds for every $p$-integrable, mean zero $B$-valued $\mathrm{rv}$ if and only if $B$ is of Rademacher type $p(1 \leq p < 2)$.

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Alejandro De Acosta. "Inequalities for $B$-Valued Random Vectors with Applications to the Strong Law of Large Numbers." Ann. Probab. 9 (1) 157 - 161, February, 1981. https://doi.org/10.1214/aop/1176994517

Information

Published: February, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0449.60002
MathSciNet: MR606806
Digital Object Identifier: 10.1214/aop/1176994517

Subjects:
Primary: 60B05

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 1 • February, 1981
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