For any distribution $P$ on $\mathbb{R}$ with c.d.f. $F$, and i.i.d. sample $X_1, \ldots, X_n \sim P$, the empirical distribution function satisfies
\begin{align*}
\sup_{t \in \mathbb{R}} |F_n(t) - F(t)| \xrightarrow{a.s.} 0 \quad \text{as } n \to \infty.
\end{align*}