Real Analysis Exchange

Representation of abstract affine functions.

Jiří Spurný

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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

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

First available in Project Euclid: 20 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Spurný, Jiří. Representation of abstract affine functions. Real Anal. Exchange 28 (2002), no. 2, 337--354.

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