If K1,...,Kn are measurable subsets of a compact measure space X and their interiors pairwise do not intersect, then the collection [Ki] is a packing in X and its packing density is If the space being packed is infinite in measure, such as Euclidean space, it is customary to define the density as the limit of densities exhibited in balls of larger and larger radii.
If Bt is the ball of radius t centered at the origin, then the density of a packing [Ki : i∈
Provided that any ball of the Euclidean space intersects only finitely many elements of the packing and that the diameters of the elements are bounded from above, the (upper, lower) density does not depend on the choice of origin, and μ(Ki∩Bt) can be replaced by μ(Ki) for every element that intersects Bt.
[1] The ball may also be replaced by dilations of some other convex body, but in general the resulting densities are not equal.
One is often interested in packings restricted to use elements of a certain supply collection.