## Ji\v r\'{i} Spurn\'y On the Dirichlet problem for functions of the first Baire class

Comment.Math.Univ.Carolinae 42,4 (2001) 721-728.

Abstract:Let $\Cal H$ be a simplicial function space on a metric compact space $X$. Then the Choquet boundary $ChX$ of $\Cal H$ is an $F_\sigma$-set if and only if given any bounded Baire-one function $f$ on $ChX$ there is an $\Cal H$-affine bounded Baire-one function $h$ on $X$ such that $h=f$ on $ChX$. This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set $X$.

Keywords: weak Dirichlet problem, function space, Choquet simplexes, Baire-one functions
AMS Subject Classification: 46A55, 31B05, 26A21