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April, 1981 On the Accompanying Laws Theorem in Banach Spaces
Aloisio Araujo, Evarist Gine, V. Mandrekar, Joel Zinn
Ann. Probab. 9(2): 202-210 (April, 1981). DOI: 10.1214/aop/1176994462


In this paper we show that a necessary and sufficient condition on a Banach space $B$ for the validity of the accompanying laws theorem is that $c_0$ is not finitely representable in $B$ or, equivalently, that $B$ is of cotype $q$ for some $q > 0$. The proof is based on a result of Maurey and Pisier on the geometry of these spaces and on a theorem about approximation in $L_p$ of Banach valued triangular arrays by finite dimensional ones.


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Aloisio Araujo. Evarist Gine. V. Mandrekar. Joel Zinn. "On the Accompanying Laws Theorem in Banach Spaces." Ann. Probab. 9 (2) 202 - 210, April, 1981.


Published: April, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0471.60014
MathSciNet: MR606983
Digital Object Identifier: 10.1214/aop/1176994462

Primary: 60F05
Secondary: 46B99 , 60B10

Keywords: accompanying laws , cotype , finite representability of $c_0$ , triangular arrays

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 2 • April, 1981
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