Much of the literature on analysis in metric spaces makes use of an assumption called *Ahlfors regularity* or *Ahlfors-David regularity*. Let $q>0$. A metric space $(X,d)$ is *Ahlfors(-David) $q$-regular* if there exists $C\geq 1$ such that $C^{-1}r^q \leq \mathcal{H}^q(B(x,r)) \leq Cr^q$ for all $x \in X$ and $r \in (0, \text{diam } X)$. Here, $\mathcal{H}^q$ denotes the $q$-dimensional Hausdorff measure. The term is so ubiquitous in the literature in this area that the origin seems impossible to trace down. I believe *David* refers to Guy David.

Can anyone fill me in on the origin of the terms and what exactly Ahlfors and David did using this type of condition?