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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convexity and Haar null sets
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by Eva Matoušková PDF
Proc. Amer. Math. Soc. 125 (1997), 1793-1799 Request permission

Abstract:

It is shown that for every closed, convex and nowhere dense subset $C$ of a superreflexive Banach space $X$ there exists a Radon probability measure $\mu$ on $X$ so that $\mu (C+x)=0$ for all $x\in X$. 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 Matoušková
  • 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
  • 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
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1793-1799
  • MSC (1991): Primary 46B10; Secondary 46B20
  • DOI: https://doi.org/10.1090/S0002-9939-97-03776-3
  • MathSciNet review: 1372040