**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