Hello everyone. I've been hitting my head against the chalk-board trying to figure this one out.

Suppose $\displaystyle E_1$ and $\displaystyle E_2$ are Lebesgue measurable. Then we want to show that:

$\displaystyle m(E_1\cup E_2)+m(E_1\cap E_2)=mE_1+mE_2$.

Recall: $\displaystyle mA=\mbox{inf }_{A\subset \cup I_n} \sum \ell (I_n)$

Also Recall: E is measurable means for any set $\displaystyle A, \; mA=m(A\cap E)+m(A\cap \widetilde E)$.

Any help on this problem would be greatly appreciated!