Approximation of measurable mappings by sequences of continuous functions
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- by Surjit Singh Khurana PDF
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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
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Additional 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