  Let $(X,d)$ be an $n$-dimensional Alexandrov space whose Hausdorff measure
$\mathcal{H}^n$ satisfies a condition giving the metric measure space
$(X,d,\mathcal{H}^n)$ a notion of having nonnegative Ricci curvature. We
examine the influence of large volume growth on these spaces and generalize
some classical arguments from Riemannian geometry showing that when the volume
growth is sufficiently large, then $(X,d,\mathcal{H}^n)$ has finite topological
type.
