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How can we recover Baire class one functions?

Part of: Real functions

Published online by Cambridge University Press:  26 February 2010

Dominique Lecomte
Dominique Lecomte
Affiliation:
Equipe d'analyse de l'Université Paris 6, Tour 46-0, boîte 186, 4, place Jussieu, 75 252 Paris cedex 05, France. E-mail: lecomte@moka.ccr.jussieu.fr
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Abstract

Let X and Y be separable metrizable spaces, and f: X→Y a function. It is wished to recover f from its values on a small set via a simple algorithm. It is shown that this is possible if f is Baire class one, and in fact a characterization is obtained. This leads to the study of sets of Baire class one functions and to a characterization of the separability of the dual space of an arbitrary Banach space.

MSC classification

Secondary: 26A21: Classification of real functions; Baire classification of sets and functions
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 171 - 198
Copyright
Copyright © University College London 2003

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