Carathéodory's criterion

Carathéodory's criterion is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory. Its statement is as follows: Let $lambda^*$ denote the Lebesgue outer measure on $mathbb\{R\}^n$, and let $Esubseteqmathbb\{R\}^n$. Then $E$ is Lebesgue measurable if and only if $lambda^*\; (A)\; =\; lambda^*\; (A\; cap\; E)\; +\; lambda^*\; (A\; setminus\; E)$ for every $Asubseteq\; mathbb\{R\}^n$.Notice that $A$ is not required to be a measurable set.

See also

*Carathéodory's theorem