The Annals of Probability

A Counterexample for Banach Space Valued Random Variables

J. Kuelbs

Full-text: Open access

Abstract

There exists a sequence of i.i.d. random variables taking values in the infinite dimensional Banach space $c_0$ satisfying the law of the iterated logarithm and failing to obey the central limit theorem.

Article information

Source
Ann. Probab., Volume 4, Number 4 (1976), 684-689.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996039

Digital Object Identifier
doi:10.1214/aop/1176996039

Mathematical Reviews number (MathSciNet)
MR451326

Zentralblatt MATH identifier
0364.60029

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G15: Gaussian processes

Keywords
Banach space valued random variables sums of independent random variables central limit theorem law of the iterated logarithm

Citation

Kuelbs, J. A Counterexample for Banach Space Valued Random Variables. Ann. Probab. 4 (1976), no. 4, 684--689. doi:10.1214/aop/1176996039. https://projecteuclid.org/euclid.aop/1176996039


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