Absolutely continuous function
= Absolutely continuous function
{wiki}
A function $f:[a,b]\to\mathbb R$ is absolutely continuous exactly when there is a function $g\in L^1(a,b)$ such that
$$
f(x)=f(a)+\int_a^x g(s)\,ds.
$$
Then $f$ is <differentiable> <almost everywhere> and $f'=g$ almost everywhere.