Baire classes of affine vector-valued functions

Ondřej F. K. Kalenda, and Jiří Spurný. "Baire classes of affine vector-valued functions." Studia Mathematica 233.3 (2016): 227-277. <http://eudml.org/doc/286103>.

@article{OndřejF2016,
abstract = {We investigate Baire classes of strongly affine mappings with values in Fréchet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of L₁-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the abstract Dirichlet problem and the weak Dirichlet problem for Baire mappings. Some of these results have weaker conclusions than their scalar versions. We also establish an affine version of the Jayne-Rogers selection theorem.},
author = {Ondřej F. K. Kalenda, Jiří Spurný},
journal = {Studia Mathematica},
keywords = {simplex; L1-predual; vector-valued Baire function; strongly affine function; Pettis integral},
language = {eng},
number = {3},
pages = {227-277},
title = {Baire classes of affine vector-valued functions},
url = {http://eudml.org/doc/286103},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Ondřej F. K. Kalenda
AU - Jiří Spurný
TI - Baire classes of affine vector-valued functions
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 3
SP - 227
EP - 277
AB - We investigate Baire classes of strongly affine mappings with values in Fréchet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of L₁-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the abstract Dirichlet problem and the weak Dirichlet problem for Baire mappings. Some of these results have weaker conclusions than their scalar versions. We also establish an affine version of the Jayne-Rogers selection theorem.
LA - eng
KW - simplex; L1-predual; vector-valued Baire function; strongly affine function; Pettis integral
UR - http://eudml.org/doc/286103
ER -