Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures
We study the classes C(α, β) and C H(α, β) of logarithmically convex measures that are a natural generalization of the notion of Boltzmann measure to an infinite-dimensional case. We prove a theorem on the characterization of these classes in terms of finite-dimensional projections of measures and d...
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| Дата: | 2002 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2002
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4068 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510197098741760 |
|---|---|
| author | Kulik, A. M. Кулик, А. М. Кулик, А. М. |
| author_facet | Kulik, A. M. Кулик, А. М. Кулик, А. М. |
| author_sort | Kulik, A. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:31Z |
| description | We study the classes C(α, β) and C H(α, β) of logarithmically convex measures that are a natural generalization of the notion of Boltzmann measure to an infinite-dimensional case. We prove a theorem on the characterization of these classes in terms of finite-dimensional projections of measures and describe some applications to the theory of random series. |
| first_indexed | 2026-03-24T02:53:10Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4068 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:53:10Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/cb/f6c80c2e15567a9ac78a903c48debbcb.pdf |
| spelling | umjimathkievua-article-40682020-03-18T20:20:31Z Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures Фильтрация и конечномерная характеризация логарифмически выпуклых мер Kulik, A. M. Кулик, А. М. Кулик, А. М. We study the classes C(α, β) and C H(α, β) of logarithmically convex measures that are a natural generalization of the notion of Boltzmann measure to an infinite-dimensional case. We prove a theorem on the characterization of these classes in terms of finite-dimensional projections of measures and describe some applications to the theory of random series. Вивчаються класи $C(α, β)$ та $C_H(α, β)$ логарифмічно опуклих мір, що є природним узагальненням поняття міри Больцмана на нескінченновимірний випадок. Доведено теорему про харак-теризацію цих класів у термінах скінченновимірних проекцій мір, отримано деякі застосування до теорії випадкових рядів. Institute of Mathematics, NAS of Ukraine 2002-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4068 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 3 (2002); 323-331 Український математичний журнал; Том 54 № 3 (2002); 323-331 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4068/4846 https://umj.imath.kiev.ua/index.php/umj/article/view/4068/4847 Copyright (c) 2002 Kulik A. M. |
| spellingShingle | Kulik, A. M. Кулик, А. М. Кулик, А. М. Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title | Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title_alt | Фильтрация и конечномерная характеризация логарифмически выпуклых мер |
| title_full | Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title_fullStr | Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title_full_unstemmed | Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title_short | Filtration and Finite-Dimensional Characterization of Logarithmically Convex Measures |
| title_sort | filtration and finite-dimensional characterization of logarithmically convex measures |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4068 |
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