*Preprint*

**Inserted:** 8 jan 2020

**Last Updated:** 8 jan 2020

**Year:** 2020

**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.

**Keywords:**
Rectifiability, bounded variation, jump set, Blowup

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