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Baire classes of affine vector-valued functions

Tom 233 / 2016

Ondřej F. K. Kalenda, Jiří Spurný Studia Mathematica 233 (2016), 227-277 MSC: 46B25, 46A55, 26A21, 54H05. DOI: 10.4064/sm8278-5-2016 Opublikowany online: 20 June 2016

Streszczenie

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.

Autorzy

  • Ondřej F. K. KalendaCharles University in Prague
    Faculty of Mathematics and Physics
    Department of Mathematical Analysis
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail
  • Jiří SpurnýCharles University in Prague
    Faculty of Mathematics and Physics
    Department of Mathematical Analysis
    Sokolovská 83
    186 75 Praha 8, Czech Republic
    e-mail

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