Let K be an open set of $\mathbb{R}^n$, then I know that I can get a countable cover by using closed cuboids $Q_i$ with a pairwise disjoint interior.
I want to show that by this fact every open set is measurable under the Lebegues measure. I suppose that I need to show that every cuboid is measurable (under the Lebesgue measure). But I don't know exactly how to proceed. Do you have a clue?