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February, 1979 Laws of Large Numbers for Tight Random Elements in Normed Linear Spaces
R. L. Taylor, Duan Wei
Ann. Probab. 7(1): 150-155 (February, 1979). DOI: 10.1214/aop/1176995156

Abstract

A strong law of large numbers is proved for tight, independent random elements (in a separable normed linear space) which have uniformly bounded $p$th moments $(p > 1)$. In addition, a weak law of large numbers is obtained for tight random elements with uniformly bounded $p$th moments $(p > 1)$ where convergence in probability for the separable normed linear space holds if and only if convergence in probability for the weak linear topology holds.

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R. L. Taylor. Duan Wei. "Laws of Large Numbers for Tight Random Elements in Normed Linear Spaces." Ann. Probab. 7 (1) 150 - 155, February, 1979. https://doi.org/10.1214/aop/1176995156

Information

Published: February, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0395.60005
MathSciNet: MR515821
Digital Object Identifier: 10.1214/aop/1176995156

Subjects:
Primary: 60B05
Secondary: 60F15, 60G99

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 1 • February, 1979
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