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A generalization of carathéodory's theorem

✍ Scribed by Imre Bárány

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
812 KB
Volume
40
Category
Article
ISSN
0012-365X

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✦ Synopsis

The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are answered.

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