Geodesic
Baire classes of affine vector-valued functions
Ondřej F. K. Kalenda 1   ; Jiří Spurný 1
1 Charles University in Prague Faculty of Mathematics and Physics Department of Mathematical Analysis Sokolovská 83 186 75 Praha 8, Czech Republic
Studia Mathematica, Tome 233 (2016) no. 3, pp. 227-277 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $L_1$-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.
DOI : 10.4064/sm8278-5-2016
Keywords: investigate baire classes strongly affine mappings values chet spaces particular validity vector valued mokobodzki result affine functions first baire class related approximation property range space further extend several results known scalar functions choquet simplices dual balls preduals vector valued concerns particular affine classes strongly affine baire mappings abstract dirichlet problem weak dirichlet problem baire mappings these results have weaker conclusions their scalar versions establish affine version jayne rogers selection theorem

Ondřej F. K. Kalenda  1   ; Jiří Spurný  1

1 Charles University in Prague Faculty of Mathematics and Physics Department of Mathematical Analysis Sokolovská 83 186 75 Praha 8, Czech Republic 
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Ondřej F. K. Kalenda; Jiří Spurný. Baire classes of affine vector-valued functions. Studia Mathematica, Tome 233 (2016) no. 3, pp. 227-277. doi: 10.4064/sm8278-5-2016

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