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Proceedings of the American Mathematical Society

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



Three convex sets

Author: Michel Talagrand
Journal: Proc. Amer. Math. Soc. 89 (1983), 601-607
MSC: Primary 46A55
MathSciNet review: 718981
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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.

References [Enhancements On Off] (What's this?)

  • [1] G. Choquet, Lectures on analysis, Benjamin, New York, 1969.
  • [2] G. A. Edgar, Extremal integral representation, J. Funct. Anal. 23 (1976), 145-165. MR 0435797 (55:8753)
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  • [4] R. R. Phelps, Lecture on Choquet's theorem, Van Nostrand, Princeton, N. J., 1966. MR 0193470 (33:1690)

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