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Continuity of Hausdorff measure on level sets

Let $\Omega\subset\mathbb{R}^2$ a open and bounded set with smooth boundary and $\phi:\Omega\to\mathbb{R}$ a smooth function such that: $\bullet$ $\phi^{-1}(0)\neq\emptyset$; $\bullet$ $\nabla\phi(x)\...
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