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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of Lusin's theorem


Author: Michael L. Wage
Journal: Proc. Amer. Math. Soc. 52 (1975), 327-332
MSC: Primary 28A10
MathSciNet review: 0379782
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Abstract: In this note we characterize $ \sigma $-finite Riesz measures that allow one to approximate measurable functions by continuous functions in the sense of Lusin's theorem. We call such measures Lusin measures and show that not all $ \sigma $-finite measures are Lusin measures.

It is shown that if a topological space $ X$ is either normal or countably paracompact, then every measure on $ X$ is a Lusin measure. A counterexample is given to show that these sufficient conditions are not necessary.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0379782-9
Article copyright: © Copyright 1975 American Mathematical Society