Theorem of Kuratowski-Suslin for measurable mappings
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- by Andrzej Wiśniewski PDF
- Proc. Amer. Math. Soc. 123 (1995), 1475-1479 Request permission
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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1475-1479
- MSC: Primary 28A20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1283566-X
- MathSciNet review: 1283566