Remark on the Abstract Dirichlet Problem for Baire-One Functions
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 55-73
MSC: 46A55, 54C30, 54H05.
DOI: 10.4064/ba53-1-6
Abstract
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.
