Let $X_1, \ldots, X_n$ be i.i.d. with c.d.f. $F$. As $n \to \infty$, \begin{align*} \sqrt{n}(F_n - F) \xrightarrow{d} G_F, \end{align*} where $G_F$ is a Gaussian process with $G_F(t) = B_{F(t)}$, satisfying \begin{align*} \operatorname{Cov}(G_F(s), G_F(t)) = F(s)(1 - F(t)) \quad \text{for } s \leq t. \end{align*}