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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

One-to-one Borel selection theorems


Authors: Marek Balcerzak and Joanna Peredko
Journal: Proc. Amer. Math. Soc. 127 (1999), 2759-2766
MSC (1991): Primary 04A15, 28A05, 54H05
Published electronically: April 23, 1999
MathSciNet review: 1487357
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Abstract: For $X=[0,1]$ we obtain new theorems stating that a Borel set in $X^2$ with large sets of large vertical and large horizontal sections admits a one-to-one Borel selection with large domain and large range. Largeness is meant mainly in measure or category sense. Our proofs combine a result of Graf and Mauldin with a modified result of Sarbadhikari.


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Additional Information

Marek Balcerzak
Affiliation: Institute of Mathematics, Łódź Technical University, al. Politechniki 11, 90-924 Łódź, Poland
Email: mbalce@krysia.uni.lodz.pl

Joanna Peredko
Affiliation: Institute of Mathematics, Łódź Technical University, al. Politechniki 11, 90-924 Łódź, Poland
Email: joannape@ck-sg.p.lodz.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04784-X
PII: S 0002-9939(99)04784-X
Keywords: One-to-one selection, Borel set, meager set, Lebesgue null set
Received by editor(s): November 3, 1997
Published electronically: April 23, 1999
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society