Open Access
August, 1976 A Counterexample for Banach Space Valued Random Variables
J. Kuelbs
Ann. Probab. 4(4): 684-689 (August, 1976). DOI: 10.1214/aop/1176996039


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.


Download Citation

J. Kuelbs. "A Counterexample for Banach Space Valued Random Variables." Ann. Probab. 4 (4) 684 - 689, August, 1976.


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

zbMATH: 0364.60029
MathSciNet: MR451326
Digital Object Identifier: 10.1214/aop/1176996039

Primary: 60B10
Secondary: 60G15

Keywords: Banach space valued random variables , central limit theorem , Law of the iterated logarithm , Sums of independent random variables

Rights: Copyright © 1976 Institute of Mathematical Statistics

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