An abstract and generalized approach to the Vitali theorem on nonmeasurable sets

Abstract

Here we present abstract formulations of two theorems of Solecki which deal with some generalizations of the classical Vitali theorem on nonmeasurable sets in spaces with transformation groups.

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