Аннотация:
For some natural classes of topological vector spaces, we show the absolute nonmeasurability
of Minkowski’s sum of certain two universal measure zero sets. This result
can be considered as a strong form of the classical theorem of Sierpiński [8] stating
the existence of two Lebesgue measure zero subsets of the Euclidean space, whose
Minkowski’s sum is not Lebesgue measurable.
Ключевые слова:Minkowski’s sum, Borel measure, universal measure zero set, absolutely
nonmeasurable set, Martin’s Axiom, generalized Luzin set, separable support of measure.