Translating Finite Sets into Convex Sets |
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Authors: | Matouskova Eva |
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Affiliation: | Mathematical Institute, Czech Academy of Sciences itná 25, CZ-11567 Prague, Czech Republic; matouse{at}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 > 0, there is a nonempty finite set F X with an arbitrarilysmall diameter, such that C contains at most .|F| points ofany translation of F. As a corollary, a separable Banach spaceX is reflexive if and only if every closed convex subset ofX with empty interior is Haar null. 2000 Mathematics SubjectClassification 46B20 (primary), 28C20 (secondary). |
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