Absolute continuity of a nondecreasing function Can anyone give me a hint on how to approach this problem? It's another problem from an old qualifying exam.
Suppose that $f\colon \mathbb R \to \mathbb R$ is nondecreasing, $\int_{\mathbb R} f' = 1$, $f(-\infty) = 0$, and $f(\infty) = 1$. Prove that $f$ is absolutely continuous on any interval $[a,b]$.

Well, there is a characterization of absolutely continuous functions: $f$ is absolutely continuous iff there is an integrable function $g$, such that $f(y)-f(x) = \int_x^y g(t)\,dt$.
But you can attack your question with more elementary tools.
