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arXiv · 2001.04675

Rectifiability of the jump set of locally integrable functions

Giacomo Del Nin
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Abstract

In this note we show that for every measurable function on $\mathbb{R}^n$ the set of points where the blowup exists and is not constant is $(n-1)$-rectifiable. In particular, for every $u\in L^1_{loc}(\mathbb{R}^n)$ the jump set $J_u$ is $(n-1)$-rectifiable.

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Giacomo Del Nin. 2020-01-14. Rectifiability of the jump set of locally integrable functions. https://arxiv.org/abs/2001.04675

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