Displaying similar documents to “Affine Baire functions on Choquet simplices”

Remark on the Abstract Dirichlet Problem for Baire-One Functions

Ondřej F. K. Kalenda (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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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...

The Dirichlet problem for Baire-one functions

Jiří Spurný (2004)

Open Mathematics

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Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.

Baire classes of affine vector-valued functions

Ondřej F. K. Kalenda, Jiří Spurný (2016)

Studia Mathematica

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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 L₁-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings,...

Compactness in the First Baire Class and Baire-1 Operators

Mercourakis, S., Stamati, E. (2002)

Serdica Mathematical Journal

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For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset...

On the Dirichlet problem for functions of the first Baire class

Jiří Spurný (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let ℋ be a simplicial function space on a metric compact space X . Then the Choquet boundary Ch X of ℋ is an F σ -set if and only if given any bounded Baire-one function f on Ch X there is an ℋ -affine bounded Baire-one function h on X such that h = f on Ch X . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set X .