An abstract and generalized approach to the Vitali theorem on nonmeasurable sets. (English) Zbl 07217180

Basu, Sanjib; Sen, Debasish

Math. Bohem. 145, No. 1, 65-70 (2020).

Summary: Here we present abstract formulations of two theorems of S. Solecki [Proc. Am. Math. Soc. 119, No. 1, 115–124 (1993; Zbl 0784.28006); ibid. 897–902 (1993; Zbl 0795.28010)] which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.

MSC:

28A05	Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28D05	Measure-preserving transformations

Keywords:

spaces with transformation groups; \(k\)-additive measurable structure; \(k\)-small system; upper semicontinuous \(k\)-small system; \(k\)-additive algebra admissible with respect to a \(k\)-small system

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