The Lyapunov theorem on convexity and its use for sign-embeddings
It is proved (Theorem 1) that for a Banach space $X$ the following statements are equialent: i) the range of every $X$-valued $\sigma$-additive non-atomic measure of finite variation has convex closure; ii) $L_1$ does not sign-embed in $X$.
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| Дата: | 1992 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1992
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8169 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512950526148608 |
|---|---|
| author | Kadets , V. М. Popov , М. М. |
| author_facet | Kadets , V. М. Popov , М. М. |
| author_sort | Kadets , V. М. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-02-26T13:58:10Z |
| description | It is proved (Theorem 1) that for a Banach space $X$ the following statements are equialent: i) the range of every $X$-valued $\sigma$-additive non-atomic measure of finite variation has convex closure; ii) $L_1$ does not sign-embed in $X$. |
| first_indexed | 2026-03-24T03:36:56Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8169 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:36:56Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5b/bd464dd7b347ddd8b5f50ee7e655fd5b.pdf |
| spelling | umjimathkievua-article-81692024-02-26T13:58:10Z The Lyapunov theorem on convexity and its use for sign-embeddings Теорема Ляпунова про опуклість та її застосування до знако-вкладень Kadets , V. М. Popov , М. М. - It is proved (Theorem 1) that for a Banach space $X$ the following statements are equialent: i) the range of every $X$-valued $\sigma$-additive non-atomic measure of finite variation has convex closure; ii) $L_1$ does not sign-embed in $X$. Доведено (теорема 1), що для банахового простору $X$ еквівалентні такі твердження: і) множина значень будь-якої $X$-значної $\sigma$-адитивної безатомної міри з скінченною варіацією має опукле замикання; іі) простір $L_1$ не можна знако-вкласти в $X$. Institute of Mathematics, NAS of Ukraine 1992-10-07 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8169 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 9 (1992); 1192-1200 Український математичний журнал; Том 44 № 9 (1992); 1192-1200 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8169/9693 Copyright (c) 1992 V. М. Kadets , М. М. Popov |
| spellingShingle | Kadets , V. М. Popov , М. М. The Lyapunov theorem on convexity and its use for sign-embeddings |
| title | The Lyapunov theorem on convexity and its use for sign-embeddings |
| title_alt | Теорема Ляпунова про опуклість та її застосування до знако-вкладень |
| title_full | The Lyapunov theorem on convexity and its use for sign-embeddings |
| title_fullStr | The Lyapunov theorem on convexity and its use for sign-embeddings |
| title_full_unstemmed | The Lyapunov theorem on convexity and its use for sign-embeddings |
| title_short | The Lyapunov theorem on convexity and its use for sign-embeddings |
| title_sort | lyapunov theorem on convexity and its use for sign-embeddings |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8169 |
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