Some Kolmogorov-Smirnov-Rényi type theorems.

In his fundamental paper (1953) [23], entitled "On the Theory of Order Statistics", A. Rényi developed a new method by means of which many important results of the theory of order statistics can be obtained with surprising simplicity. The essential novelty of his method is that it reduces the problems connected with order statistics to the study of sums of mutually independent random variables. Chapter 1 of this thesis contains a review of this method. The above mentioned method has also enabled Rényi to give an interesting improvement of the Kolmogorov - Smirnov theorems