Geodesic
On Some Limit Theorems Involving the Empirical Distribution Function
Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 739-741

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Let X1 ..., Xn be mutually independent random variables with a common continuous distribution function F (t). Let Fn(t) be the corresponding empirical distribution function, that isFn(t) = (number of Xi ≤ t, 1 ≤ i ≤ n)/n.Using a theorem of Manija [4], we proved among others the following statement in [1]. 
Csörgo, Miklós. On Some Limit Theorems Involving the Empirical Distribution Function. Canadian mathematical bulletin, Tome 10 (1967) no. 5, pp. 739-741. doi: 10.4153/CMB-1967-077-0
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[1] 1. Csörgo, M.(1966). Exact and limiting probability distributions of some Smirmovtype statistics. Canad. Math. Bull. 8, pp. 93-103. Google Scholar

[2] 2. Donsker, M. D. (1955). Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov Theorems. Ann. Math. Statist. 23, pp. 277-281. Google Scholar

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[4] 4. Manija, G. M., (1944). Obobschenije Kriterija A. N. Kolmogorova dlja otcenkizakona racpredelenija po empirichesk imdannym. Dokl. Akad. Nauk. SSSR 69, pp. 495-497. Google Scholar

[5] 5. Quade, Dana (1966). On the asymptotic power of the one-sample Kolmogorov-Smirnov tests. Ann. Math. Statist. 36, pp. 1000-1018. Google Scholar

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