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Additive Families of Low Borel Classes and Borel Measurable Selectors

Published online by Cambridge University Press:  20 November 2018

J. Spurný  and
M. Zelený
J. Spurný
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Czech Republice-mail: spurny@karlin.mff.cuni.czzeleny@karlin.mff.cuni.cz
M. Zelený
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Czech Republice-mail: spurny@karlin.mff.cuni.czzeleny@karlin.mff.cuni.cz
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Abstract

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An important conjecture in the theory of Borel sets in non-separable metric spaces is whether any point-countable Borel-additive family in a complete metric space has a $\sigma $-discrete refinement. We confirm the conjecture for point-countable $\Pi _{3}^{0}$-additive families, thus generalizing results of R. W. Hansell and the first author. We apply this result to the existence of Borel measurable selectors for multivalued mappings of low Borel complexity, thus answering in the affirmative a particular version of a question of J. Kaniewski and R. Pol.

Keywords

54H0554E35σ-discrete refinementBorel-additive familymeasurable selection
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 1 , 01 March 2011 , pp. 180 - 192
Copyright
Copyright © Canadian Mathematical Society 2011

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