### ON A BAD DESCRIPTIVE STRUCTURE OF MINKOWSKI’S SUM OF CERTAIN SMALL SETS IN A TOPOLOGICAL VECTOR SPACE

**ALEXANDER B. KHARAZISHVILI**

*Theory of Stochastic Processes*

*Vol. 14 (30), no. 2, 2008, pp. 35–41*

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 Sierpi´nski [8] stating the existence of two Lebesgue measure zero subsets of the Euclidean space, whose Minkowski’s sum is not Lebesgue measurable.

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