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arXiv · 2607.02348

Eliminating positive-measure level sets by small Lipschitz perturbations

Sorina Barza·Martin Lind
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Abstract

We establish a new regularity phenomenon of continuous functions. Specifically, given any continuous function $f$ and arbitrary $\epsilon>0$, we construct a Lipschitz perturbation $g_\epsilon$ whose Lipschitz seminorm is less than $\epsilon$ such that every level set of $f+g_\epsilon$ has Lebesgue measure zero.

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Sorina Barza, Martin Lind. 2026-07-02. Eliminating positive-measure level sets by small Lipschitz perturbations. https://arxiv.org/abs/2607.02348

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