Theorem of Kuratowski-Suslin for measurable mappings. II
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- by Andrzej Wiśniewski PDF
- Proc. Amer. Math. Soc. 124 (1996), 3703-3710 Request permission
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
- 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
- K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
- Leo F. Epstein, A function related to the series for $e^{e^x}$, J. Math. Phys. Mass. Inst. Tech. 18 (1939), 153–173. MR 58, DOI 10.1002/sapm1939181153
- M. Suslin, Sur une définition des ensembles mesurables B sans nombres transfinis, C. R. Acad. Sci. Paris 164 (1917), 89.
- A. Wiśniewski, Theorem of Kuratowski-Suslin for measurable mappings, Proc. Amer. Math. Soc. 123 (1995), 1475–1479.
Additional Information
- Andrzej Wiśniewski
- Affiliation: Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland
- Email: awisniew@uoo.univ.szczecin.pl
- Received by editor(s): November 28, 1994
- Received by editor(s) in revised form: April 14, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3703-3710
- MSC (1991): Primary 28A05, 28A20; Secondary 28C20, 60B05, 60B11
- DOI: https://doi.org/10.1090/S0002-9939-96-03467-3
- MathSciNet review: 1342048