In the proof of Theorem 3.18, verify that (hat{F}_{n}(t)-F(t) geq hat{F}_{n}(t)-Fleft(t_{i-1}ight)-varepsilon). Theorem 3.18 (Glivenko and Cantelli). Let

In the proof of Theorem 3.18, verify that \(\hat{F}_{n}(t)-F(t) \geq \hat{F}_{n}(t)-F\left(t_{i-1}ight)-\varepsilon\).

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Theorem 3.18 (Glivenko and Cantelli). Let X,..., Xn be a set of indepen- dent and identically distributed random variables from a distribution F, and let Fn be the empirical distribution function computed on X,..., Xn. Then F-F a.c. 0.