Real Analysis Exchange

Representation of abstract affine functions.

Jiří Spurný

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Abstract

It is known that any subspace \(\H\) of the space of continuous functions on a compact set can be represented as the space of affine continuous functions defined on the state space of \(\H\). The aim of this paper is to generalize this result for abstract affine functions of various descriptive classes (Borel, Baire etc.). The important step in the proof is to derive results on the preservation of the descriptive properties of topological spaces under perfect mappings. The main results are applied on the space of affine functions on compact convex sets and on approximation of semicontinuous and Baire--one abstract affine functions.

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 337-354.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963799

Mathematical Reviews number (MathSciNet)
MR2009758

Zentralblatt MATH identifier
1057.46005

Subjects
Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 46A55: Convex sets in topological linear spaces; Choquet theory [See also 52A07] 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
Function spaces state space barycentric formula Baire and Borel functions affine functions

Citation

Spurný, Jiří. Representation of abstract affine functions. Real Anal. Exchange 28 (2002), no. 2, 337--354. https://projecteuclid.org/euclid.rae/1184963799


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