Remark on the Abstract Dirichlet Problem for Baire-One Functions

• Autorzy: Ondřej F. K. Kalenda
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 46A55: Convex sets in topological linear spaces; Choquet theory
• 54C30: Real-valued functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 1
• Strony: 55-73

Daty

wydano

2005

Twórcy

autor

Ondřej F. K. Kalenda

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/ba53-1-6