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Published January 2010 | public
Journal Article

Variation on a theorem by Carathéodory


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.

Additional Information

© 2010 University College London. Received May 26 2009. Thanks to Professors Gil Kalai and Imre Barany for helpful communications. The author was supported in part by NSF Award CCF-0829909.

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