  I show that a $d$-dimensional definable set $S\subseteq\mathbb{R}^n$ in an
o-minimal expansion of the ordered field of real numbers satisfies the volume
estimate $\mathcal{H}^d(\{x\in S:\lVert x\rVert<r\})\leq Cr^d$, where
$\mathcal{H}^d$ denotes the $d$-dimensional Hausdorff measure on $\mathbb{R}^n$
and $C$ is a constant depending on $S$. Coupled with the theorem of Bishop and
Stoll, this result gives a quick proof of the GAGA theorem of Peterzil and
Starchenko in the case of o-minimal expansions of the ordered field of real
numbers.
