On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space
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 Sierpinski [8] stating the existence of two Lebesgue measure zero sub...
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| Дата: | 2008 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/4550 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space / A.B. Kharazishvili // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 2. — С. 35–41. — Бібліогр.: 22 назв.— англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 Sierpinski [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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