| Suppose we are given a distribution of non-overlapping discs on the plane, and suppose that the plane is partitioned into regions (not necessarily of finite area) surrounding each disc. For each one, calculate the ratio of the area of the disc to the area of the region. This is the **the density of the distribution in that region**. Then, no matter what the partition is, ** the density of the overall distribution cannot be greater than than the maximum of its densities in the various regions**. | The density of the distribution cannot be greater than the maximum density among the smaller regions. | |