Choquet like sets in function spaces. (Q1407226)

Many problems involving spaces of functions are dealt with by transferring the problem to the state space, which is a subset of the dual space. Convexity of the state space means that concepts such as exposed subsets, extremal subsets, and parallel, split and complementary faces, can be brought to bear. The authors move somewhat in the opposite direction, by seeking natural versions of these concepts for the common domain of the functions under consideration, even though this domain need not admit any convex structure. In other words, Choquet theory is developed without state spaces. The article culminates with a definition and characterization of simpliciality for function spaces, and a characterization of Choquet subsets in the domain of a space of harmonic functions.