Baire classes of affine vector-valued functions

被引:6
作者
Kalenda, Ondrej F. K. [1 ]
Spurny, Jiri [1 ]
机构
[1] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague 18675 8, Czech Republic
关键词
simplex; L-1-predual; vector-valued Baire function; strongly affine function; Pettis integral; DIRICHLET PROBLEM; BANACH-SPACES; REAL STRUCTURE; L1; SIMPLICES; SUBSPACES; EXTREME; THEOREM; DUALS; BALL;
D O I
10.4064/sm8278-5-2016
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We investigate Baire classes of strongly affine mappings with values in Frechet 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.
引用
收藏
页码:227 / 277
页数:51
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