Calculus of Variations and Geometric Measure Theory
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G. Del Nin

Rectifiability of the jump set of locally integrable functions

created by delnin on 08 Jan 2020
modified on 03 Jun 2021


Accepted Paper

Inserted: 8 jan 2020
Last Updated: 3 jun 2021

Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Year: 2020
Doi: 10.2422/2036-2145.202002_006

ArXiv: 2001.04675 PDF


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.

Keywords: Rectifiability, bounded variation, jump set, Blowup


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