  Let $\Omega$ be an open set in a metric measure space $X$. Our main result
gives an equivalence between the validity of a weighted Hardy-Sobolev
inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect
to Whitney covers of $\Omega$. Important ingredients in the proof include the
use of a discrete convolution as a capacity test function and a Maz'ya type
characterization of weighted Hardy-Sobolev inequalities.
