On sets where lip(f) is infinite for monotone continuous functions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916108429164544 |
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| author | Rmoutil, Martin Zürcher, Thomas |
| author_facet | Rmoutil, Martin Zürcher, Thomas |
| contents | Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz constant of f is equal to infinity exactly at points of A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sets where lip(f) is infinite for monotone continuous functions Rmoutil, Martin Zürcher, Thomas Classical Analysis and ODEs Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz constant of f is equal to infinity exactly at points of A. |
| title | On sets where lip(f) is infinite for monotone continuous functions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.15388 |