On the Kolmogorov and Smirnov Limit Theorems for Discontinuous Distribution Functions

Abstract

1. Introduction. Let X1, X2,..., XN be N independent random variables with the same distribution function F (x). SN (X) is the empirical distribution function, ie, SN (X)= k/N if exactly k of the N values Xi are less than or equal to x. It is of theoretical and practical ...