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August, 1984 On the Law of Large Numbers in 2-Uniformly Smooth Banach Spaces
Bernard Heinkel
Ann. Probab. 12(3): 851-857 (August, 1984). DOI: 10.1214/aop/1176993233


In this paper we extend the Kolmogorov strong law of large numbers to random variables taking their values in a 2-uniformly smooth Banach space $(B, \| \|)$. In our result, the convergence of the classical series of variances is replaced by the convergence of the series having general term $\sup\{Ef^2(X_n)/n^2: \|f\|_{B'} \leq 1\}.$


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Bernard Heinkel. "On the Law of Large Numbers in 2-Uniformly Smooth Banach Spaces." Ann. Probab. 12 (3) 851 - 857, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0545.60015
MathSciNet: MR744239
Digital Object Identifier: 10.1214/aop/1176993233

Primary: 60B12
Secondary: 46B20

Keywords: 2-uniformly smooth Banach space , Strong law of large numbers , type 2 space

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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