  We study a capacity theory based on a definition of a Riesz potential in
metric spaces with a doubling measure. In this general setting, we study the
basic properties of the Riesz capacity, including monotonicity, countable
subadditivity and several convergence results. We define a modified version of
the Hausdorff measure and provide lower bound and upper bound estimates for the
capacity in terms of the modified Hausdorff content.
