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Measurable functions and almost continuous functions

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Abstract

I show that if (X, μ) is a Radon measure space and Y is a metric space, then a function from X to Y is μ-measurable iff it is almost continuous (=Lusin measurable). I discuss other cases in which measurable functions are almost continuous.

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Authors and Affiliations

  1. Mathematics Department, University of Essex, co4 3sq, Colchester, England

    D. H. Fremlin

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  1. D. H. Fremlin
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Part of the work of this paper was done during a visit to Japan supported by the United Kingdom Science Research Council and Hokkaido University

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Fremlin, D.H. Measurable functions and almost continuous functions. Manuscripta Math 33, 387–405 (1981). https://doi.org/10.1007/BF01798235

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  • DOI: https://doi.org/10.1007/BF01798235

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