  We provide an empirical process theory for locally stationary processes over
nonsmooth function classes. An important novelty over other approaches is the
use of the flexible functional dependence measure to quantify dependence. A
functional central limit theorem and nonasymptotic maximal inequalities are
provided. The theory is used to prove the functional convergence of the
empirical distribution function (EDF) and to derive uniform convergence rates
for kernel density estimators both for stationary and locally stationary
processes. A comparison with earlier results based on other measures of
dependence is carried out.
