Open Access
Translator Disclaimer
August, 1976 The Law of Large Numbers and the Central Limit Theorem in Banach Spaces
J. Hoffmann-Jorgensen, G. Pisier
Ann. Probab. 4(4): 587-599 (August, 1976). DOI: 10.1214/aop/1176996029

Abstract

Let $X_1, X_2, \cdots$ be independent random variables with values in a Banach space $E$. It is then shown that Chung's version of the strong law of large numbers holds, if and only if $E$ is of type $p$. If the $X_n$'s are identically distributed, then it is shown that the central limit theorem is valid, if and only if $E$ is of type 2. Similar results are obtained for vectorvalued martingales.

Citation

Download Citation

J. Hoffmann-Jorgensen. G. Pisier. "The Law of Large Numbers and the Central Limit Theorem in Banach Spaces." Ann. Probab. 4 (4) 587 - 599, August, 1976. https://doi.org/10.1214/aop/1176996029

Information

Published: August, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0368.60022
MathSciNet: MR423451
Digital Object Identifier: 10.1214/aop/1176996029

Subjects:
Primary: 60F05
Secondary: ‎46E15, 60B10

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.4 • No. 4 • August, 1976
Back to Top