A solution of the abstract Dirichlet problem for Baire-one functions

Let X be a compact convex subset of a locally convex space. We show that any bounded Baire-one function defined on ext X can be extended to an affine Baire-one function on X if and only if X is a Choquet simplex and ext X satisfies a certain topological property. © 2005 Elsevier Inc. All rights reserved