  We investigate, by "a la Marcinkiewicz" techniques applied to the
(asymptotic) density function, how dense systems of equal spheres of $\rb^{n},
n \geq 1,$ can be partitioned at infinity in order to allow the computation of
their density as a true limit and not a limsup. The density of a packing of
equal balls is the norm 1 of the characteristic function of the systems of
balls in the sense of Marcinkiewicz. Existence Theorems for densest sphere
packings and completely saturated sphere packings of maximal density are given
new direct proofs.
