 Carathéodory's criterion

A set $E$ is measurable for an outer measure ${\mu }^{\ast }$ when every set $A$ is split additively by $E$:The measurable sets form a sigma-algebra, and the restriction of ${\mu }^{\ast }$ to it is a complete measure.

Carathéodory's criterion is a theorem related to the characterization of measurable sets in the context of measure theory. Specifically, it provides a way to determine whether a set is Lebesgue measurable.