Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T16:41:01.020Z Has data issue: false hasContentIssue false

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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