A. Kirtadze

On the Method of Direct Products in the Theory of Quasi-Invariant Measures

Abstract:
For invariant (quasi-invariant) $\sigma$-finite measures on an uncountable group $(G,\cdot)$, the behaviour of small sets with respect to the operation "$\cdot$" is studied. Some classes of non-commutative groups $(G,\cdot)$ are discussed especially, by using a representation of the original group in the form of a direct product of its two subgroups, one of which is commutative.

Keywords:
Non-commutative group, quasi-invariant measure, measure zero set, direct product of groups, negligible set, absolutely negligible set.

MSC 2000: 28A05, 28D05