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.References
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G. Choquet, Lectures on analysis, Benjamin, New York, 1969.
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- Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
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