On the approximation of measurable functions by continuous functions
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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 phrasesτ-smooth measures Lindelöf subsets
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- [BP] Bessaga C., Pelczyńsky A.,Infinite-dimensional Topology, Polish Scientific Publishers, 1975.Google Scholar
- [DU] Diestel J., Uhl J. J., Jr.,Vector Measures, Mathematical Surveys, 15, Amer. Math. Soc., 1977.Google Scholar
- [GP] Gardner R. J., Pfeffer W. F.,Borel Measures, Handbook of settheoretic topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, 1984, pp. 961–1043.Google Scholar
- [H] Halmos P. R.,Measure Theory, Van Nostrand, 1950.Google Scholar
- [M] Munkres J. R.,Topology, a first course, Prentice-Hall, 1975.Google Scholar