Let $X_n$ be a series of random variables converging in law to $X$. Let $F_n,F$ be the corresponding distribution functions, then if the variable $X$ is continuous (takes every value with probability 0) $F_n$ converges uniformly to $F$.
I know that convergence in law implies the convergence of $F_n$ to $F$ in every point where $F$ is continuous (here then in every point), but how can you prove that the convergence is uniform?
thank you!
