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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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/4550 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735669266219008 |
|---|---|
| author | Kharazishvili, A.B. |
| author_facet | Kharazishvili, A.B. |
| citation_txt | 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. |
| collection | DSpace DC |
| description | 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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| first_indexed | 2025-12-07T19:50:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4550 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-12-07T19:50:02Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kharazishvili, A.B. 2009-12-03T16:35:43Z 2009-12-03T16:35:43Z 2008 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. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4550 519.21 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. en Інститут математики НАН України On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space Article published earlier |
| spellingShingle | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space Kharazishvili, A.B. |
| title | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space |
| title_full | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space |
| title_fullStr | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space |
| title_full_unstemmed | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space |
| title_short | On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space |
| title_sort | on a bad descriptive structure of minkowski’s sum of certain small sets in a topological vector space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4550 |
| work_keys_str_mv | AT kharazishviliab onabaddescriptivestructureofminkowskissumofcertainsmallsetsinatopologicalvectorspace |