On selectors nonmeasurable with respect to quasiinvariant measures

Abstract

We discuss a question on the existence of partial \(\mu\)-nonmeasurable \(H\)-selectors, where \(\mu\) is a given nonzero \(\sigma\)-finite measure defined on some \(\sigma\)-algebra of subsets of a set \(E\) and quasiinvariant under an uncountable group \(G\) of transformations of \(E\), and \(H\) is an arbitrary countable subgroup of \(G\).