Is it true $\mu (A+B) = \mu (A) + \mu(B) $ for bounded sets $ A, B \subset R $ where $\mu $ is Lebesgue outer measure.
2026-02-22 21:51:09.1771797069
Is it true $\mu (A+B) = \mu (A) + \mu(B) $ for bounded sets $ A, B \subset R $
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Take $A=[0,1] \cup [2,3], B=[0,2]$.
Then $A+B = [0,5]$, but $\mu^* (A+B) = 5$ whereas $\mu^* A + \mu^* B = 4$.