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October, 1977 An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series
Jean-Pierre Gabriel
Ann. Probab. 5(5): 779-786 (October, 1977). DOI: 10.1214/aop/1176995719

Abstract

R. Pyke raised the question of the convergence of series indexed by filtering sets. This paper contains a generalization of an inequality of Marcinkiewicz-Zygmund for a certain class of filtering sets, which gives rise to the theory of series for this type of set.

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Jean-Pierre Gabriel. "An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series." Ann. Probab. 5 (5) 779 - 786, October, 1977. https://doi.org/10.1214/aop/1176995719

Information

Published: October, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0376.60057
MathSciNet: MR445608
Digital Object Identifier: 10.1214/aop/1176995719

Subjects:
Primary: 60G50
Secondary: 60G45

Keywords: Almost everywhere convergence , characteristic functions , Filtering sets , Independent random variables , isomorphism

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • October, 1977
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