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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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8169 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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