# open sets and measurability

Let $$A$$ be a subset of $$mathbb{R}$$ with $$m^*(A) (where $$m^*$$ denotes the Lebesgue outer measure). Is it true that for every open subset $$Osubset mathbb{R}$$ we always have the equality $$m^*(O)=m^*(Ocap A)+m^*(Ocap A^c)$$ ? Does anybody have an idea or clue? Thanks in advance.