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Theorem of Kuratowski-Suslin for measurable mappings. II

Author(s): Andrzej Wisniewski
Journal: Proc. Amer. Math. Soc. 124 (1996), 3703-3710.
MSC (1991): Primary 28A05, 28A20; Secondary 28C20, 60B05, 60B11
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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:

1.: K. Kuratowski, Topology I, Academic Press-PWN, New York-Warszawa, 1966. MR 36:840
2.: K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York, 1967. MR 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: 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
Copyright of article: Copyright 1996, American Mathematical Society


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