Point simpliciality in Choquet theory on nonmetrizable compact spaces

Abstract

Let H be a function space on a compact space K. The set of simpliciality of H is the set of all points of K for which there exists a unique maximal representing measure.

Properties of this set were studied by M. Bačák in the paper Point simpliciality in Choquet representation theory, Illinois J.

Math. 53 (2009) 289-302, mainly for K metrizable. We study properties of the set of simpliciality for K nonmetrizable.

Keywords

• Point simpliciality
• Choquet theory
• nonmetrizable compact spaces