Corollary 1

— For a set A to be negligible, it is necessary and sufficient that it be locally negligible and of finite outer measure.

The condition is obviously necessary. Conversely, if it is satisfied then A is contained in an integrable open set G, which is the union of a negligible set N and a sequence $(K_n)$ of compact sets (§ 4, No. 6, Cor. 2 of Th. 4); since $A \cap N$ and the sets $A \cap K_n$ are negligible, the same is true of their union A.