  The probabilistic powerdomain $\mathbf V X$ on a space $X$ is the space of
all continuous valuations on $X$. We show that, for every quasi-continuous
domain $X$, $\mathbf V X$ is again a quasi-continuous domain, and that the
Scott and weak topologies then agree on $\mathbf V X$. This also applies to the
subspaces of probability and subprobability valuations on $X$. We also show
that the Scott and weak topologies on the $\mathbf V X$ may differ when $X$ is
not quasi-continuous, and we give a simple, compact Hausdorff counterexample.
