  The aim of the present paper is to prove that the family of all closed
nonempty subsets of a complete probabilistic metric space $L$ is complete with
respect to the probabilistic Pompeiu-Hausdorff metric $H$. The same is true for
the families of all closed bounded, respectively compact, nonempty subsets of
$L$. If $L$ is a complete random normed space in the sense of \v{S}erstnev,
then the family of all nonempty closed convex subsets of $L$ is also complete
with respect to $H$.
