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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of Lusin’s theorem
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by Michael L. Wage
Proc. Amer. Math. Soc. 52 (1975), 327-332
DOI: https://doi.org/10.1090/S0002-9939-1975-0379782-9

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.
References
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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 327-332
  • MSC: Primary 28A10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0379782-9
  • MathSciNet review: 0379782