Strong uniform consistency rates of kernel estimators of cumulative distribution functions

In this paper we consider the uniform strong consistency, along with a rate, of the cumulative distribution function (CDF) estimator. We extend the extended Glivenko–Cantelli lemma (for empirical distribution function) in Fabian and Hannan (1985 Fabian, V., Hannan, J. (1985). Introduction to Probability and Mathematical Statistics. New York: Wiley, ISBN-13:978-0471250234. Google Scholar], pp. 80–83) to the kernel estimator of the CDF.