Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda

Bulletin of the Polish Academy of Sciences. Mathematics (2005)

  • Volume: 53, Issue: 1, page 55-73
  • ISSN: 0239-7269

Abstract

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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.

How to cite

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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 53.1 (2005): 55-73. <http://eudml.org/doc/281116>.

@article{OndřejF2005,
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.},
author = {Ondřej F. K. Kalenda},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Choquet simplex; affine Baire-one function; abstract Dirichlet problem; extreme points; Lindelöf space; -set},
language = {eng},
number = {1},
pages = {55-73},
title = {Remark on the Abstract Dirichlet Problem for Baire-One Functions},
url = {http://eudml.org/doc/281116},
volume = {53},
year = {2005},
}

TY - JOUR
AU - Ondřej F. K. Kalenda
TI - Remark on the Abstract Dirichlet Problem for Baire-One Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2005
VL - 53
IS - 1
SP - 55
EP - 73
AB - 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.
LA - eng
KW - Choquet simplex; affine Baire-one function; abstract Dirichlet problem; extreme points; Lindelöf space; -set
UR - http://eudml.org/doc/281116
ER -

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