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The structure of measurable mappings on metric spaces

Author: Andrzej Wiśniewski
Journal: Proc. Amer. Math. Soc. 122 (1994), 147-150
MSC: Primary 28A20
MathSciNet review: 1201807
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Abstract: The purpose of this paper is to investigate the conditions under which every measurable mapping on a metric space X with the measure $ \mu $ is a limit of a sequence of continuous mappings, with respect to the convergence $ \mu $-almost everywhere.

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  • [1] L. V. Kantorovich and G. P. Akilov, \cyr Funktsional′nyĭ analiz., Izdat. “Nauka”, Moscow, 1977 (Russian). Second edition, revised. MR 0511615
  • [2] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
  • [3] Ĭ. Ī. Gīhman and A. V. Skorohod, The theory of stochastic processes. I, Springer-Verlag, New York-Heidelberg, 1974. Translated from the Russian by S. Kotz; Die Grundlehren der mathematischen Wissenschaften, Band 210. MR 0346882
  • [4] S. Hartman and J. Mikusiński, The theory of Lebesgue measure and integration, Enlarged ed., translated from Polish by Leo F. Boron. International Series of Monographs on Pure and Applied Mathematics, Vol. 15, Pergamon Press, New York-Oxford-London-Paris; Pań-stwowe Wydawnictwo Naukowe, Warsaw, 1961. MR 0123662
  • [5] K. Jänich, Topology, Springer-Verlag, New York, Berlin, Heidelberg, and New York, 1980.
  • [6] M. E. Munroe, Introduction to measure and integration, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1953. MR 0053186

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Keywords: Metric spaces, Borel measures, Borel mappings, measurable mappings, continuous mappings
Article copyright: © Copyright 1994 American Mathematical Society