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arXiv · 2505.22975

$\mathbf{C^2}$-Lusin approximation of convex functions: one variable case

Paweł Goldstein·Piotr Hajłasz
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Abstract

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 $\Vert f-g\Vert_\infty<\varepsilon$.

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Paweł Goldstein, Piotr Hajłasz. 2025-05-29. $\mathbf{C^2}$-Lusin approximation of convex functions: one variable case. https://arxiv.org/abs/2505.22975

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