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.References
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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