Fundamental theorem of calculus for Lebesgue integration
= Fundamental theorem of calculus for Lebesgue integration
If $g\in L^1(a,b)$, then $F(x)=F(a)+\int_a^xg(s)\,ds$ is <absolutely continuous function>[absolutely continuous] and satisfies $F'=g$ <almost everywhere>. Conversely, every absolutely continuous function has this form.