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.

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.

 

Approximation of measurable mappings by sequences of continuous functions
HTML articles powered by AMS MathViewer

by Surjit Singh Khurana
Proc. Amer. Math. Soc. 131 (2003), 937-939
DOI: https://doi.org/10.1090/S0002-9939-02-06583-8
Published electronically: June 13, 2002

Abstract:

Let $X$ be a completely regular Hausdorff space, $\mu$ a positive, finite Baire measure on $X$, and $E$ a separable metrizable locally convex space. Suppose $f: X \to E$ is a measurable mapping. Then there exists a sequence of functions in $C_{b}(X) \otimes E$ which converges to $f$ a.e. $[ \mu ]$. If the function $f$ is assumed to be weakly continuous and the measure $\mu$ is assumed to be $\tau$-smooth, then a separability condition is not needed.
References
Similar Articles
Bibliographic Information
  • Surjit Singh Khurana
  • Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
  • Email: khurana@math.uiowa.edu
  • Received by editor(s): August 18, 2001
  • Received by editor(s) in revised form: October 10, 2001
  • Published electronically: June 13, 2002
  • Communicated by: Claudia M. Neuhauser
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 937-939
  • MSC (2000): Primary 60B05, 28C15; Secondary 60B11, 28B05
  • DOI: https://doi.org/10.1090/S0002-9939-02-06583-8
  • MathSciNet review: 1937432