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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Theorem of Kuratowski-Suslin
for measurable mappings. II


Author: Andrzej Wisniewski
Journal: Proc. Amer. Math. Soc. 124 (1996), 3703-3710
MSC (1991): Primary 28A05, 28A20; Secondary 28C20, 60B05, 60B11
MathSciNet review: 1342048
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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to describe these $\mu $-measurable mappings on a separable complete metric space with the Borel measure $\mu $, which transform every $\mu $-measurable set onto a $\mu $-measurable one. The obtained results are a generalization of the classical outcomes of Suslin and Kuratowski and the results from our previous paper.


References [Enhancements On Off] (What's this?)

  • 1. K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751 (36 #840)
  • 2. K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684 (37 #2271)
  • 3. K. R. Parthasarathy, Introduction to probability and measure, Macmillan Co. of India, Dehli, 1977. MR 58:31322
  • 4. M. Suslin, Sur une définition des ensembles mesurables B sans nombres transfinis, C. R. Acad. Sci. Paris 164 (1917), 89.
  • 5. A. Wi\'{s}niewski, Theorem of Kuratowski-Suslin for measurable mappings, Proc. Amer. Math. Soc. 123 (1995), 1475-1479. CMP 95:07

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Additional Information

Andrzej Wisniewski
Affiliation: Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland
Email: awisniew@uoo.univ.szczecin.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03467-3
PII: S 0002-9939(96)03467-3
Keywords: Borel sets, measurable and non-measurable sets, Borel mappings, measurable mappings, absolute continuity of measures.
Received by editor(s): November 28, 1994
Received by editor(s) in revised form: April 14, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society