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-alpha function.

This generalizes a result of E. M.

Alfsen from [2]. We also consider extensions of vector-valued mappings, thus generalizing another result of E.

M. Alfsen.

Keywords

• dirichlet
• problem
• extreme
• points
• non-continuous
• functions