Example of strictly subadditive lebesgue outer measure One of the properties of the Lebesgue outer measure is that it is subadditive and not countably additive. In fact, I have read that even when the sets A_i  are disjoint, there is still generally strict inequality.
I was just wondering if anyone can give me an example of this, any set of disjoint real number intervals that I can think of always lead to a equality (hence countable additivity).

A Bernstein set, $A\subseteq[0,1]$ has the property that both $A$ and $[0,1]\setminus A$ have outer measure $1$.
