The weak Dirichlet problem for Baire functions

Spurný, Jiří

doi:10.1090/S0002-9939-06-08683-7

The weak Dirichlet problem for Baire functions
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by Jiří Spurný

Proc. Amer. Math. Soc. 134 (2006), 3153-3157

DOI: https://doi.org/10.1090/S0002-9939-06-08683-7

Published electronically: June 5, 2006

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Abstract:

Let $X$ be a simplex and $K$ 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 $X$. Moreover, $h$ can be chosen in such a way that $h(X)\subset \overline {\operatorname {co}} f(K)$.

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