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VARIATION ON A THEOREM BY CARATHÉODORY

  • Leonard J. Schulman (a1)
Abstract

Carathéodory’s theorem on small witnesses for convex hulls of sets is shown to have a natural analogue for finitely supported measures. Contrast is drawn with the much larger witnesses required for multisets, as shown by Bárány and Perles.

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[1]Bárány, I. and Larman, D. G., Convex bodies, economic cap coverings, random polytopes. Mathematika 35 (1988), 274291.
[2]Bárány, I. and Perles, M., The Caratheodory number for the k-core. Combinatorica 10(2) (1990), 185194.
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[12]Stancu, A., The floating body problem. Bull. London Math. Soc. 38 (2006), 839846.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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