  Let G be a real reductive group and G/H a unimodular homogeneous G space with
a closed connected subgroup H. We establish estimates for the invariant measure
on G/H. Using these, we prove that all smooth vectors in the Banach
representation L^p(G/H) of G are functions that vanish at infinity if and only
if G/H is of reductive type. An application to lattice counting on G/H is
presented.
