Rectifiability of the jump set of locally integrable functions
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 $(n1)$rectifiable. In particular, for every $u\in L^1_{loc}(\mathbb{R}^n)$ the jump set $J_u$ is $(n1)$rectifiable.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.04675
 Bibcode:
 2020arXiv200104675D
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Analysis of PDEs;
 Primary: 26B05;
 Secondary: 26A15;
 26B30
 EPrint:
 6 pages