The convergence in the central limit theorem is uniform because the limiting cumulative distribution function is continuous. If the third central moment exists and is finite, then the speed of convergence is at least on the order of (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.
the convergence in the central limit theorem is uniform because the limiting cumulative distribution function is continuous if the third central moment exists and is finite then the speed of convergence is at least on the order of (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