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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation of measurable mappings by sequences of continuous functions


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 131 (2003), 937-939
MSC (2000): Primary 60B05, 28C15; Secondary 60B11, 28B05
Published electronically: June 13, 2002
MathSciNet review: 1937432
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06583-8
PII: S 0002-9939(02)06583-8
Keywords: Baire measures, $ \tau$-smooth measures, support of a measure
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
Article copyright: © Copyright 2002 American Mathematical Society