Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A generalization of Lusin’s theorem
HTML articles powered by AMS MathViewer

by Michael L. Wage PDF
Proc. Amer. Math. Soc. 52 (1975), 327-332 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A10
  • Retrieve articles in all journals with MSC: 28A10
Additional 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