Let $(A_n)_{n \geq 1}$ be a sequence of random variables with c.d.f.s $F_n$, and let $A$ be a random variable with continuous c.d.f. $F$. If $A_n \xrightarrow{d} A$ as $n \to \infty$, then
\begin{align*}
\sup_{t \in \mathbb{R}} |F_n(t) - F(t)| \to 0.
\end{align*}