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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of bimeasurable functions in terms of universally measurable sets


Author: R. B. Darst
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
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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}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0274694-X
Keywords: Bimeasurable function, Borel function, Borel set, continuum hypothesis, infinitely differentiable function, probability measure, separable complete metric space, universally measurable function, universally measurable set, universal null set
Article copyright: © Copyright 1971 American Mathematical Society