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

Abstract

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.

Keywords

• solution
• abstract
• Dirichlet
• problem
• Baire-one
• functions