Given a set $E$ is Lebesgue measurable, and $E$=$E_1$\cup$E_2$, if $m(E)$ is less than infinity, $m(E)$ = $m^{*}(E_1) + m^{*}(E_2)$,where $m(E)$ is the Lebesgue measure of $E$,and $m^{*}(E_1)$ and $m^{*}(E_2)$ are the outer measure of $E_1$ and $E_2$ how to prove that $E_1$ and $E_2$ are measurable.
the measurability of sets given their union are measurable
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measure-theory
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0oh, yeah.thanks Clayton. – 2012-12-29