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arXiv · 1402.4443

Dimension of gradient measures

Dmitriy M. Stolyarov·Michal Wojciechowski
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Abstract

We prove that if pure derivatives with respect to all coordinates of a function on $\mathbb{R}^n$ are signed measures, then their lower Hausdorff dimension is at least $n-1$. The derivatives with respect to different coordinates may be of different order.

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Dmitriy M. Stolyarov, Michal Wojciechowski. 2014-02-18. Dimension of gradient measures. https://arxiv.org/abs/1402.4443

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