Let A http://upload.wikimedia.org/math/4/2...9b30f02246.png R^{n}and let |A|_{e}be the Lebesgue outer measure.

Suppose A, B http://upload.wikimedia.org/math/4/2...9b30f02246.png R^{n}and d(A,B)>0. How do I prove that |A http://upload.wikimedia.org/math/d/3...2ec3ce0dac.png B|_{e}=|A|_{e}+|B|_{e}?

Having thought about this problem for days, I still can't solve it. Any suggestion?