✦ LIBER ✦

On Closed Coverings of Simplexes

✍ Scribed by Yakar Kannai

Book ID: 124881120
Publisher: Society for Industrial and Applied Mathematics
Year: 1970
Tongue: English
Weight: 382 KB
Volume: 19
Category: Article
ISSN: 0036-1399
DOI: 10.2307/2099394

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Simple proofs of four theorems of \(\mathbf{K y}\) Fan on covering of simplexes by closed sets are presented. Open versions and reformulations of these theorems are also given. 1993 Academic Press, Inc.

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## Abstract We consider closed bounded Choquet simplexes of tight measures on Hausdorff spaces. If the extreme boundary is closed, then each element is the barycenter of a uniquely determined tight probability measure on the extreme points. Consequently, on Hausdorff spaces tight exchangeable measu

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## Abstract The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non‐empty co‐r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Le