Article contents
Some properties of maximal measures on compact convex sets
Published online by Cambridge University Press: 24 October 2008
Abstract
Let be a maximal measure on a compact convex set K, K* be the state space of the space of all continuous functions f: KK ℝ which are affine in the first variable, 1 be the -algebra on K generated by the Baire sets and the compact extremal subsets of K, and = {BeK1}. Then
(i) For any fixed continuous function g:K ℝ and -almost all x in K, there is a closed face of K containing x on which g is constant.
(ii) The image of under the map :KK* defined by f, (x) = f(x, x) is the unique maximal measure on K* representing its barycentre
(iii) induces a measure on (eK) satisfying certain regularity conditions.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 297 - 305
- Copyright
- Copyright © Cambridge Philosophical Society 1983
References
REFERENCES
- 5
- Cited by