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Theorem of Kuratowski-Suslin for measurable mappings


Author: Andrzej Wiśniewski
Journal: Proc. Amer. Math. Soc. 123 (1995), 1475-1479
MSC: Primary 28A20
MathSciNet review: 1283566
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Abstract: The purpose of this paper is to describe these Borel mappings on a separable complete metric space X which transform every measurable set (with respect to some measure $ \mu $ on X) onto a measurable one. It is shown that a one-to-one Borel mapping f on X fulfills the above property if and only if the measure $ \mu $ is absolutely continuous with respect to the measure $ {\mu _f}$ (an image of $ \mu $ under the mapping f). Our results are a generalization of the classical results of Suslin and Kuratowski.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1283566-X
Keywords: Borel sets, measurable and nonmeasurable sets, Borel mappings, measurable mappings, absolute continuity of measures, admissible translations of measures
Article copyright: © Copyright 1995 American Mathematical Society