Choquet Simplices Research Articles

Baire bijections of extreme points generated by small-bound isomorphisms of simplex spaces

We show that small-bound isomorphisms of spaces of affine continuous functions on Choquet simplices with Lindel?f boundaries induce Baire measurable bijections of their sets of extreme points.

Baire classes of affine vector-valued functions

We investigate Baire classes of strongly affine mappings with values in Fr\'echet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki's result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of $L_1$-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the abstract Dirichlet problem and the weak Dirichlet problem for Baire mappings. Some of these results have weaker conclusions than their scalar versions. We also establish an affine version of the Jayne-Rogers selection theorem.

A characterization of unbounded Choquet simplices

A characterization of unbounded Choquet simplices

Some results on the geometry of Choquet simplices

In this paper, we give some properties of Choquet simplices which lead to the characterization of the closed Choquet simplices of ℝn.