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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Measure and category approximations for $ C$-sets


Author: V. V. Srivatsa
Journal: Trans. Amer. Math. Soc. 278 (1983), 495-505
MSC: Primary 04A15; Secondary 03E15, 28A99, 54H05
MathSciNet review: 701507
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Abstract: The class of $ C$-sets in a Polish space is the smallest $ \sigma $-field containing the Borel sets and closed under operation $ (\mathcal{A})$. In this article we show that any $ C$-set in the product of two Polish spaces can be approximated (in measure and category), uniformly over all sections, by sets generated by rectangles with one side a $ C$-set and the other a Borel set. Such a formulation unifies many results in the literature. In particular, our methods yield a simpler proof of a selection theorem for $ C$-sets with $ {G_\delta }$-sections due to Burgess [4].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0701507-4
PII: S 0002-9947(1983)0701507-4
Keywords: Analytic set, $ C$-set, selections
Article copyright: © Copyright 1983 American Mathematical Society