We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function. We also study the analogous questions for functions of higher Baire classes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-6,
author = {Ond\v rej F. K. Kalenda},
title = {Remark on the Abstract Dirichlet Problem for Baire-One Functions},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {55-73},
zbl = {1118.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-6}
}
Ondřej F. K. Kalenda. Remark on the Abstract Dirichlet Problem for Baire-One Functions. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 55-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-6/