Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems
Doob  has given heuristically an appealing methodology for deriving asymptotic theorems on the difference between the empirical distribution function calculated from a sample and the actual distribution function of the population being sampled. In particular he has applied these methods to deriving the well known theorems of Kolmogorov  and Smirnov . In this paper we give a justification of Doob's approach to these theorems and show that the method can be extended to a wide class of such asymptotic theorems.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177729445
Digital Object Identifier: doi:10.1214/aoms/1177729445
Mathematical Reviews number (MathSciNet): MR47288
Zentralblatt MATH identifier: 0046.35103