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On the Lp convergence of sums of independent random variables

Published online by Cambridge University Press:  24 October 2008

Peter Hall
Peter Hall
Affiliation:
University of Melbourne†
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Abstract

Let {Xnj, 1 ≤ j ≤ kn} be independent random variables with zero means and satisfying . Let p ≥ 1. We prove that

if and only if, for all ε > 0,

and we use this result to obtain necessary and sufficient conditions for the Lp convergence of sums of non-negative, independent random variables.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 439 - 446
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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