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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.

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Approximation of measurable mappings by sequences of continuous functions
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by Surjit Singh Khurana PDF
Proc. Amer. Math. Soc. 131 (2003), 937-939 Request permission


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.
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Additional Information
  • Surjit Singh Khurana
  • Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
  • Email:
  • 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:
  • MathSciNet review: 1937432