I have two questions on measure theory:
How do you show that a monotone increasing real function on a closed interval [a, b] is Lebesgue measurable function.
Suppose A is a subset of the closed interval [0,1] which is dense. (That is, the closure of A is all of [0,1].) suppose U is an open set with A⊆U. Must it be true that m(U) ≥ 1?