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Carathéodory's Theorem

Published online by Cambridge University Press:  20 November 2018

W. D. Cook
Affiliation:
Dalhousie University, Halifax, Nova Scotia
R. J. Webster
Affiliation:
Dalhousie University, Halifax, Nova Scotia
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Despite the abundance of generalizations of Carathéodory's theorem occurring in the literature (see [1]), the following simple generalization involving infinite convex combinations seems to have passed unnoticed. Boldface letters denote points of Rn and Greek letters denote scalars.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Reay, J. R., Generalizations of a theorem of Carathéodory, Memoir. Amer. Math. Soc. 54, 1965.Google Scholar