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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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


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.
  • S. D. Chatterji, Singularity and absolute continuity of measures in infinite dimensional spaces, Probability theory on vector spaces (Proc. Conf., Trzebieszowice, 1977) Lecture Notes in Math., vol. 656, Springer, Berlin, 1978, pp. 17–23. MR 521017
  • Srishti D. Chatterji and Vidyadhar Mandrekar, Quasi-invariance of measures under translation, Math. Z. 154 (1977), no. 1, 19–29. MR 443066, DOI 10.1007/BF01215109
  • Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • I. P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Akademie-Verlag, Berlin, 1954 (German). MR 0063424
  • K. R. Parthasarathy, Introduction to probability and measure, Macmillan Co. of India, Ltd., Delhi, 1977. MR 0651012, DOI 10.1007/978-1-349-03365-2
  • G. E. Šilov and B. L. Gurevič, Integral, mera i proizvodnaya. Obshchaya teoriya, Second revised edition, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0219686
  • A. V. Skorohod, Integration in Hilbert space, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 79, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by Kenneth Wickwire. MR 0466482, DOI 10.1007/978-3-642-65632-3
  • M. Suslin, Sur une definition des ensembles mesurables B sans nombres transfinis, C. R. Acad. Sci. Paris 164 (1917), 89.
  • Joel Zinn, Admissible translates of stable measures, Studia Math. 54 (1975/76), no. 3, 245–257. MR 400376, DOI 10.4064/sm-54-3-245-257
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1475-1479
  • MSC: Primary 28A20
  • DOI:
  • MathSciNet review: 1283566