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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 $m(M)=m(E)+m(M\setminus E)$

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    What definition of measurable set are you using?2012-08-22
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    $E\subseteq\mathbb {R}$ is measurable if for any $A\subseteq \mathbb R$, $m(A)=m(A\cap E)+ m(A\cap E^c)$2012-08-22
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    In this case, this problem seems to need nothing more than checking (for $E$) and applying (for $M$) the definition. What's stumping you?2012-08-22
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    where the use of $M$ is measurable?2012-08-22
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    Hint: Via this definition, a set is measurable iff its complement is measurable, and iff its relative complement with a measurable set is measurable.2012-08-22

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