could any one help me to solve the problem?
$E\subseteq M\subseteq \mathbb {R}$, $M$ is measurable given that outer measure $m$ of $M<\infty$, we need to show $E$ is measurable iff $m(M)=m(E)+m(M\setminus E)$
could any one help me to solve the problem?
$E\subseteq M\subseteq \mathbb {R}$, $M$ is measurable given that outer measure $m$ of $M<\infty$, we need to show $E$ is measurable iff $m(M)=m(E)+m(M\setminus E)$