A characterization of bimeasurable functions in terms of universally measurable sets
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- by R. B. Darst
- Proc. Amer. Math. Soc. 27 (1971), 566-571
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274694-X
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Abstract:
The purpose of this note is to show, assuming the continuum hypothesis, that a Borel function, $f$, mapping a Borel subset, ${D_f}$, of a separable complete metric space, ${M_1}$, into a separable complete metric space, ${M_2}$, maps Borel subsets of ${D_f}$ onto Borel subsets of ${M_2}$ if, and only if, $f$ maps universally measurable subsets of ${D_f}$ onto universally measurable subsets of ${M_2}$.References
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- Stefan Mazurkiewicz, Travaux de topologie et ses applications, PWN—Éditions Scientifiques de Pologne, Warsaw, 1969 (French). Comité de rédaction: K. Borsuk, R. Engelking, B. Knaster, K. Kuratowski, J. Loś, R. Sikorski. MR 0250248 N. Lusin, Leçons sur les ensembles analytiques et leurs applications, Gauthier-Villars, Paris, 1930.
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 566-571
- MSC: Primary 28.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274694-X
- MathSciNet review: 0274694