Question: Let $\mu$ be a finite positive Borel measure on $\mathbb{R}$ that is singular to Lebesgue measure. Show that $$\lim_{r\to 0^+} \frac{\mu([x-r,x+r])}{2r}=+\infty$$ for $\mu$-almost every $x\in\mathbb{R}$.
By Folland Theorem 3.22, I know that the set of these $x$ is $m$-null, but I don't know why it is $\mu$-a.e.