Remark on the abstract Dirichlet problem for Baire-one functions

• Autorzy: Kalenda O. F. K.

Identyfikatory

DOI

10.4064/ba53-1-6

• 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.

Słowa kluczowe

EN

Choquet simplex; affine Baire-one function; abstract Dirichlet problem; extreme points; Lindelof space; H-set

PL

sympleks Choqueta; punkt ekstremalny; przestrzeń Lindelofa; H-zbiór

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 1
• Strony: 55--73
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Kalenda O. F. K.

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

Bibliografia

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