For iid observations with CDF F and empirical CDF F_n,let D_n=sup_x|F_n(x)−F(x)| and T_n=√nD_n. I:the law of T_n is the same for all continuous F. II:D_n→0 almost surely. Which hold?
For continuous F,the probability integral transform reduces the empirical comparison to the uniform case,so the null law is distribution-free. The Glivenko–Cantelli theorem gives uniform almost-sure convergence of F_n to F. Both hold. **C**.
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