This is an exercise from a real analysis book that is supposed to help you with entrance exams. I am trying to teach myself.
Suppose $X$ is a set of real numbers, and $B$ is the Boresl $\sigma$-algebra. $m$ and $n$ are two measures on $(X,B)$ such that $m((a,b))=n((a,b))< \infty$ whenever $-\infty<a<b<\infty$. I want to show that $m(A)=n(A)$ for $A\in B$
I have an idea of letting $S$ be a family of sets where the condition of the measures is satisfied, that is $m((a,b))=n((a,b))$. I think showing that S is a $\sigma$-algebra should be enough.
I am having trouble with the complement part because of the interval. I am pretty comfortable working with sets, but the intervals are throwing me off a bit.
Thanks for any input!