Measure and category approximations for 𝐶-sets

Srivatsa, V. V.

doi:10.1090/S0002-9947-1983-0701507-4

Measure and category approximations for $C$-sets
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by V. V. Srivatsa

Trans. Amer. Math. Soc. 278 (1983), 495-505

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

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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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