$\mathbf{C^2}$-Lusin approximation of convex functions: one variable case
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908639663489024 |
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| author | Goldstein, Paweł Hajłasz, Piotr |
| author_facet | Goldstein, Paweł Hajłasz, Piotr |
| contents | We prove that if $f:(a,b)\to\mathbb{R}$ is convex, then for any $\varepsilon>0$ there is a convex function $g\in C^2(a,b)$ such that $|\{f\neq g\}|<\varepsilon$ and $\Vert f-g\Vert_\infty<\varepsilon$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbf{C^2}$-Lusin approximation of convex functions: one variable case Goldstein, Paweł Hajłasz, Piotr Classical Analysis and ODEs 26A51, 41A29, 26B25 We prove that if $f:(a,b)\to\mathbb{R}$ is convex, then for any $\varepsilon>0$ there is a convex function $g\in C^2(a,b)$ such that $|\{f\neq g\}|<\varepsilon$ and $\Vert f-g\Vert_\infty<\varepsilon$. |
| title | $\mathbf{C^2}$-Lusin approximation of convex functions: one variable case |
| topic | Classical Analysis and ODEs 26A51, 41A29, 26B25 |
| url | https://arxiv.org/abs/2505.22975 |