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On a bad descriptive structure of Minkowski’s sum
of certain small sets in a topological vector space
Alexander B. Kharazishvili A.Razmadze Mathematical Institute, M.Alexidze Street, 1, Tbilisi 0193, Georgia
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.
Образец цитирования:
Alexander B. Kharazishvili, “On a bad descriptive structure of Minkowski’s sum
of certain small sets in a topological vector space”, Theory Stoch. Process., 14(30):2 (2008), 35–41
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp142 https://www.mathnet.ru/rus/thsp/v14/i2/p35
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Страница аннотации: | 90 | PDF полного текста: | 43 | Список литературы: | 21 |
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