The Dirichlet problem on compact convex sets

Abstract

Let X be a compact convex set with the set ext X of extreme points being Lindelof and f: ext X -> F be a bounded Baire mapping with values in a Frechet space F. We present a necessary and sufficient condition for f to be extended to a strongly affine Baire function on the whole set X. (C) 2021 Elsevier Inc.

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Keywords

• Compact convex set
• Vector-valued Baire function
• Strongly affine function
• Pettis integral