Geodesic
Remark on the Abstract Dirichlet Problem for Baire-One Functions
Ondřej F. K. Kalenda1
1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 55-73 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba53-1-6
Keywords: study possibility extending bounded baire one function set extreme points compact convex set affine baire one function related questions complete solutions these questions within class choquet simplices introduced stacey particular get example choquet simplex its set extreme points borel bounded baire one function set extreme points extended affine baire one function study analogous questions functions higher baire classes

Ondřej F. K. Kalenda 1

1 Department of Mathematical Analysis Faculty of Mathematics and Physics Charles University Sokolovská 83 186 75 Praha 8, Czech Republic 
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     title = {Remark on the {Abstract} {Dirichlet} {Problem} for
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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) no. 1, pp. 55-73. doi: 10.4064/ba53-1-6

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