Alexander Kharazishvili

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

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.

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

MSC 2000: 28A05, 28D05