We prove that given a fixed radius r, the set of isometry-invariant
probability measures supported on ``periodic'' radius r-circle packings of
the hyperbolic plane is dense in the space of all isometry-invariant
probability measures on the space of radius r-circle packings. By a periodic
packing, we mean one with cofinite symmetry group. As a corollary, we prove the
maximum density achieved by isometry-invariant probability measures on a space
of radius r-packings of the hyperbolic plane is the supremum of densities of
periodic packings. We also show that the maximum density function varies
continuously with radius.Comment: 25 page
