Disjoint ball decomposition modulo null sets
= Disjoint ball decomposition modulo null sets
Every open set of finite <Lebesgue measure> in Euclidean space is covered, up to a <null set>, by countably many pairwise disjoint open balls contained in it. At each stage cover a compact subset of the open remainder, choose a packing with the <Wiener covering lemma>, and remove its closed balls. A fixed positive fraction of the remaining measure is removed each time, while sphere boundaries are null.