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 $(n-1)$-rectifiable. In particular, for every $u\in L^1_{loc}(\mathbb{R}^n)$ the jump set $J_u$ is $(n-1)$-rectifiable.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.04675
- arXiv:
- arXiv:2001.04675
- Bibcode:
- 2020arXiv200104675D
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Analysis of PDEs;
- Primary: 26B05;
- Secondary: 26A15;
- 26B30
- E-Print:
- V1: 6 pages V2: 7 pages