On differential properties of mappings into a Banach space
We prove that the Rieffel sharpness condition for a Banach space E is necessary and sufficient for an arbitrary Lipschitz function f: [a, b]→E to be differentiable almost everywhere on a segment [a, b]. We establish that, in the case where the sharpness condition is not satisfied, the major part (in...
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5023 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511220025524224 |
|---|---|
| author | Bondar, A. V. Бондарь, А. В. Бондарь, А. В. |
| author_facet | Bondar, A. V. Бондарь, А. В. Бондарь, А. В. |
| author_sort | Bondar, A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:23:18Z |
| description | We prove that the Rieffel sharpness condition for a Banach space E is necessary and sufficient for an arbitrary Lipschitz function f: [a, b]→E to be differentiable almost everywhere on a segment [a, b]. We establish that, in the case where the sharpness condition is not satisfied, the major part (in the category sense) of Lipschitz functions has no derivatives at any point of the segment [a, b]. |
| first_indexed | 2026-03-24T03:09:25Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5023 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:09:25Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/94/bd0ed7226dfd495f0337510b1f1c7994.pdf |
| spelling | umjimathkievua-article-50232020-03-18T21:23:18Z On differential properties of mappings into a Banach space О дифференциальных свойствах отображений в банахово пространство Bondar, A. V. Бондарь, А. В. Бондарь, А. В. We prove that the Rieffel sharpness condition for a Banach space E is necessary and sufficient for an arbitrary Lipschitz function f: [a, b]→E to be differentiable almost everywhere on a segment [a, b]. We establish that, in the case where the sharpness condition is not satisfied, the major part (in the category sense) of Lipschitz functions has no derivatives at any point of the segment [a, b]. Доведено, що умова гостроти Ріффела для банахового простору E є необхідною і достатньою для того, щоб довільна ліпшіцова функція f: [a, b]→E була диференційовною майже всюди на відрізку [a, b]. Встановлено, що у випадку відсутності властивості гостроти більшість (у сенсі категорії) ліпшіцових функцій не мають похідної в жодній точці відрізка [a, b]. Institute of Mathematics, NAS of Ukraine 1997-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5023 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 4 (1997); 500–509 Український математичний журнал; Том 49 № 4 (1997); 500–509 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5023/6745 https://umj.imath.kiev.ua/index.php/umj/article/view/5023/6746 Copyright (c) 1997 Bondar A. V. |
| spellingShingle | Bondar, A. V. Бондарь, А. В. Бондарь, А. В. On differential properties of mappings into a Banach space |
| title | On differential properties of mappings into a Banach space |
| title_alt | О дифференциальных свойствах отображений в банахово пространство |
| title_full | On differential properties of mappings into a Banach space |
| title_fullStr | On differential properties of mappings into a Banach space |
| title_full_unstemmed | On differential properties of mappings into a Banach space |
| title_short | On differential properties of mappings into a Banach space |
| title_sort | on differential properties of mappings into a banach space |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5023 |
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