Convexity and Haar null sets

Author:
Eva Matousková

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1793-1799

MSC (1991):
Primary 46B10; Secondary 46B20

MathSciNet review:
1372040

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for every closed, convex and nowhere dense subset of a superreflexive Banach space there exists a Radon probability measure on so that for all . In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a closed convex nowhere dense set which is not Haar null.

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Additional Information

**Eva Matousková**

Affiliation:
Department of Mathematical Analysis, Charles University, Sokolovská 83 , 18600 Prague, Czech Republic;
Institut für Mathematik, Johannes Kepler Universität, Altenbergerstraße, A-4040 Linz, Austria

Email:
eva@caddo.bayou.uni-linz.ac.at

DOI:
https://doi.org/10.1090/S0002-9939-97-03776-3

Keywords:
Superreflexive Banach spaces,
convexity,
Haar null sets

Received by editor(s):
February 22, 1995

Received by editor(s) in revised form:
January 8, 1996

Additional Notes:
The author was partially supported by the grant GAČR 201/94/0069 and by a grant of the Austrian Ministry of Education.

Communicated by:
Dale Alspach

Article copyright:
© Copyright 1997
American Mathematical Society