Point simpliciality in Choquet representation theory

Abstract

Let $\mathcal{H}$ be a function space on a compact space $K$. If $\mathcal{H}$ is not simplicial, we can ask at which points of $K$ there exist unique maximal representing measures. We shall call the set of such points the set of simpliciality. The aim of this paper is to examine topological, algebraic and measure-theoretic properties of the set of simpliciality. We shall also define and investigate sets of points enjoying other simplicial-like properties.