**Alexander Kharazishvili**

## The Algebraic Sum of Two
Absolutely Negligible Sets can be an Absolutely Nonmeasurable Set

**Abstract:**

We prove that there exist two absolutely negligible subsets $A$ and $B$ of the
real line $R$, whose algebraic sum $A + B$ is an absolutely nonmeasurable subset
of $R$. We also obtain some generalization of this result and formulate a
relative open problem for uncountable commutative groups.

**Keywords:**

Invariant measure, quasi-invariant measure, absolutely negligible set,
absolutely nonmeasurable set, extension of measure.

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