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TRANSLATING FINITE SETS INTO CONVEX SETS

Published online by Cambridge University Press:  28 November 2001

EVA MATOUšKOVA
EVA MATOUšKOVA
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Žitná 25, CZ-11567 Prague, Czech Republic; matouse@matsrv.math.cas.cz
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Abstract

Let X be a reflexive Banach space, and let C ⊂ X be a closed, convex and bounded set with empty interior. Then, for every δ > 0, there is a nonempty finite set F ⊂ X with an arbitrarily small diameter, such that C contains at most δ · |F| points of any translation of F. As a corollary, a separable Banach space X is reflexive if and only if every closed convex subset of X with empty interior is Haar null.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 711 - 714
Copyright
© The London Mathematical Society 2001

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