**Alexander Kharazishvili**

## On Absolutely Negligible Sets in
Uncountable Solvable Groups

**Abstract:**

Absolutely negligible sets in uncountable groups are considered in connection
with the measure extension problem (for $\sigma$-finite invariant or
quasi-invariant measures). In particular, it is proved that, for any uncountable
solvable group $(G,\cdot)$, there exists a countable covering

of $G$ consisting of $G$-absolutely negligible sets.

**Keywords:**

Solvable group, invariant measure, quasi-invariant measure, absolutely
negligible set, Sierpi\'nski's problem.

**MSC 2000:** 28A05, 28D05