On the Dirichlet problem of extreme points for non-continuous functions

Abstract

Let X be a compact convex set and f be a bounded function defined on the set ext X of extreme points of X. We present a necessary and sufficient condition ensuring that f can be extended to a strongly affine Baire– function.

This generalize a result of E.M. Alfsen from.

We also consider extensions of vector–valued mappings, generalizing thus another result of E.M. Alfsen.

Keywords

• Dirichlet problem
• extreme points