It's the Ex.24 in Chapter 3Real Analysis(Stein) Does anyone know how to solve it?

Suppose F is an increasing function on [a,b]

a). Prove that we can write F= $\displaystyle F_A +F_C +F_J$

where $\displaystyle F_A$ is absolutely continuous; $\displaystyle F_C$ is continuous, but $\displaystyle F'_C = 0$ for a.e. x;

$\displaystyle F_J$ is a jump function;

b). Moreover, each component is uniquely determined up to an additive constant.