On the Dirichlet problem for functions of the first Baire class
Spurný, Jiří
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 721-728 / Harvested from Czech Digital Mathematics Library
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Let $\Cal H$ be a simplicial function space on a metric compact space $X$. Then the Choquet boundary $\operatorname{Ch}X$ of $\Cal H$ is an $F_\sigma$-set if and only if given any bounded Baire-one function $f$ on $\operatorname{Ch}X$ there is an $\Cal H$-affine bounded Baire-one function $h$ on $X$ such that $h=f$ on $\operatorname{Ch}X$. This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set $X$.

Publié le : 2001-01-01
Classification:  26A21,  31B05,  31C45,  46A55 
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     author = {Ji\v r\'\i\ Spurn\'y},
     title = {On the Dirichlet problem for functions of the first Baire class},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {721-728},
     zbl = {1090.46500},
     mrnumber = {1883380},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119287}
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Spurný, Jiří. On the Dirichlet problem for functions of the first Baire class. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 721-728. http://gdmltest.u-ga.fr/item/119287/

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