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VARIATION ON A THEOREM BY CARATHÉODORY

Part of: General convexity

Published online by Cambridge University Press:  10 December 2009

Leonard J. Schulman
Leonard J. Schulman*
Affiliation:
Caltech, MC305-16, Pasadena, CA 91125, U.S.A. (email: schulman@caltech.edu)
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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.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 169 - 172
Copyright
Copyright © University College London 2010

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References

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