Volume of fluid method

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 $E\subseteq {\mathbb{ℝ}}^n$. Then $E$ is Lebesgue measurable if and only if ${\lambda }^{*}(A)={\lambda }^{*}(A\cap E)+{\lambda }^{*}(A\cap E^c)$ for every $A\subseteq {\mathbb{ℝ}}^n$. Notice that $A$ is not required to be a measurable set.

See also

• Carathéodory's theorem

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