  In the following paper, we prove a dimension bound on the singular set of a
Radon measure assuming its doubling ratio converges uniformly on compact sets.
More precisely, we prove that if a Radon measure is $n$-Uniformly
Asymptotically Doubling, then $\dim(\mathcal{S}_{\mu}) \leq n-3$, where
$\mathcal{S}_{\mu}$ is the singular set of the measure.
