Existence of open quasiconvex subsets dense in a given space
The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.
We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...
A class of closed, bounded, convex sets in the Banach space is shown to be a complete PCA set.
In this paper we give general methods of construction of various equivalent minimal pairs of compact convex sets that are not translates of one another.