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On the approximation of measurable functions by continuous functions

  • J. M. Aldaz
Article

Abstract

We present a characterization of the completed Borel measure spaces for which every measurable function, with values in a separable Frechet space, is the almost everywhere limit of a sequence of continuous functions. From this characterization one can easily obtain results that have appeared recently in the literature, in a more general form. We also examine what happens when the range is a subset of an arbitrary Banach space, and show that this case often reduces to the separable case.

1980 Mathematics Subject Classification (1985 Revision)

28C15 54D20 

Key words and phrases

τ-smooth measures Lindelöf subsets 

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Copyright information

© Springer 1996

Authors and Affiliations

  1. 1.Departmento de Matemáticas Faciltad de CienciasUniversidad Autónoma de MadridMadridSpain

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