One-to-one Borel selection theorems
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- by Marek Balcerzak and Joanna Peredko PDF
- Proc. Amer. Math. Soc. 127 (1999), 2759-2766 Request permission
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.References
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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
- Received by editor(s): November 3, 1997
- Published electronically: April 23, 1999
- Communicated by: Frederick W. Gehring
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2759-2766
- MSC (1991): Primary 04A15, 28A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9939-99-04784-X
- MathSciNet review: 1487357