. . "Remark on the abstract Dirichlet problem for Baire-one functions"@en . "19"^^ . "11320" . "540733" . . "0239-7269" . "1"^^ . . "Remark on the abstract Dirichlet problem for Baire-one functions" . . . "Kalenda, Ond\u0159ej" . . . "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 simplicies 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" . . "RIV/00216208:11320/05:00001395!RIV06-MSM-11320___" . "1"^^ . "PL - Polsk\u00E1 republika" . . . "1" . . "Pozn\u00E1mka o abstraktn\u00EDm Dirichletov\u011B probl\u00E9mu pro funkce prvn\u00ED Baireovy t\u0159\u00EDdy"@cs . "Remark on the abstract Dirichlet problem for Baire-one functions"@en . "55;73" . . "RIV/00216208:11320/05:00001395" . "P(GA201/03/0933), Z(MSM0021620839)" . "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 simplicies 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"@en . "Remark; abstract; Dirichlet; problem; Baire-one; functions"@en . . "Remark on the abstract Dirichlet problem for Baire-one functions" . . . . "Pozn\u00E1mka o abstraktn\u00EDm Dirichletov\u011B probl\u00E9mu pro funkce prvn\u00ED Baireovy t\u0159\u00EDdy"@cs . "53" . . "Abstraktn\u00ED Dirichlet\u016Fv probl\u00E9m pro funkce prvn\u00ED Baireovy t\u0159\u00EDdy je vy\u0159e\u0161en v r\u00E1mci Staceyho simplex\u016F. Analogick\u00E9 v\u00FDsledky jsou dok\u00E1z\u00E1ny pro funkce vy\u0161\u0161\u00EDch t\u0159\u00EDd."@cs . "Bulletin of the Polish Academy of Sciences. Mathematics" . . "[C8A561E870AD]" . .