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arXiv · 2112.15376

Characterization of rectifiability via Lusin type approximation

Andrea Marchese·Andrea Merlo
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Abstract

We prove that a Radon measure $\mu$ on $\mathbb{R}^n$ can be written as $\mu=\sum_{i=0}^n\mu_i$, where each of the $\mu_i$ is an $i$-dimensional rectifiable measure if and only if for every Lipschitz function $f:\mathbb{R}^n\to\mathbb{R}$ and every $\varepsilon>0$ there exists a function $g$ of class $C^1$ such that $\mu(\{x\in\mathbb{R}^n:g(x)\neq f(x)\})<\varepsilon$.

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Andrea Marchese, Andrea Merlo. 2021-12-31. Characterization of rectifiability via Lusin type approximation. https://doi.org/10.2140/apde.2024.17.2109

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