We know that Lebesgue Outer Measure is countably sub-additive. It is not even finitely additive. I am trying to find two sets of real numbers which are disjoint and yet $\mu ^*(A\cup B) = \mu^*(A) +\mu^*(B)$ doesn't hold.
2026-03-28 08:31:08.1774686668
Lebesgue Outer Measure is not Finitely Additive.
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