Caratheodory measurability criterion
= Caratheodory measurability criterion
{c}
{wiki=Carathéodory's_criterion}
= Caratheodory criterion
{c}
{synonym}
A set $E$ is measurable for an <outer measure> $\mu^*$ when every set $A$ is split additively by $E$:
$$
\mu^*(A)=\mu^*(A\cap E)+\mu^*(A\setminus E).
$$
The measurable sets form a <sigma-algebra>, and the restriction of $\mu^*$ to it is a complete measure.