Measure and category approximations for -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 -sets in a Polish space is the smallest -field containing the Borel sets and closed under operation . In this article we show that any -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 -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 -sets with -sections due to Burgess [**4**].

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1983-0701507-4

Keywords:
Analytic set,
-set,
selections

Article copyright:
© Copyright 1983
American Mathematical Society