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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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