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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Three convex sets
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by Michel Talagrand PDF
Proc. Amer. Math. Soc. 89 (1983), 601-607 Request permission

Abstract:

We construct a Choquet simplex $K$ such that there is a universally measurable affine function $f$ on $K$, which satisfies the barycentric calculus, and is zero on the set of extreme points, but is not identically zero. We also construct a closed convex bounded set of a Banach space without extreme points, but such that each point is the barycenter of a maximal measure. Finally, we construct a closed bounded set $L$ of ${l^1}({\mathbf {R}})$ and a maximal measure on $L$ which is supported by a weak Baire set which contains no extreme points.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 601-607
  • MSC: Primary 46A55
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718981-5
  • MathSciNet review: 718981