structural:scholar_edition
Convergence to the limit

The convergence in the central limit theorem is uniform because the limiting cumulative distribution function is continuous. If the third central moment E {\textstyle \operatorname {E} \left} exists and is finite, then the speed of convergence is at least on the order of 1 / n {\textstyle 1/{\sqrt {n}}} (see Berry–Esseen theorem). Stein's method can be used not only to prove the central limit theorem, but also to provide bounds on the rates of convergence for selected metrics.