Three convex sets
Author:
Michel Talagrand
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We construct a Choquet simplex 
such that there is a universally measurable affine function 
on 
, 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 
of 
and a maximal measure on 
which is supported by a weak Baire set which contains no extreme points.
- [1] G. Choquet, Lectures on analysis, Benjamin, New York, 1969.
- [2] G. A. Edgar, Extremal integral representations, J. Functional Analysis 23 (1976), no. 2, 145–161. MR 0435797, https://doi.org/10.1016/0022-1236(76)90072-0
- [3] Richard Haydon, Some more characterizations of Banach spaces containing 𝑙₁, Math. Proc. Cambridge Philos. Soc. 80 (1976), no. 2, 269–276. MR 423047, https://doi.org/10.1017/S0305004100052890
- [4] Robert R. Phelps, Lectures on Choquet’s theorem, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0193470
, Math. Proc. Cambridge Philos. Soc. 80 (1976), 269-276. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A55
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0718981-5
Article copyright:
© Copyright 1983
American Mathematical Society
