The Annals of Probability

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

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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.

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 779-786.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995719

Digital Object Identifier
doi:10.1214/aop/1176995719

Mathematical Reviews number (MathSciNet)
MR445608

Zentralblatt MATH identifier
0376.60057

JSTOR
links.jstor.org

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G45

Keywords
Filtering sets isomorphism independent random variables characteristic functions almost everywhere convergence

Citation

Gabriel, Jean-Pierre. 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 (1977), no. 5, 779--786. doi:10.1214/aop/1176995719. https://projecteuclid.org/euclid.aop/1176995719


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