The weak Dirichlet problem for Baire functions

Abstract

Let $X$ be a simplex and $K$ be a compact subset of the set of all extreme points of $X$. We show that any bounded function $f$ of Baire class $\alpha$ on $K$ can be extended to a function $h$ of affine class $\alpha$ on $X$.

Keywords

• Dirichlet
• problem
• Baire
• functions