  In this paper, we develop a general machinery for finding explicit uniform
probability and moment bounds on sub-additive positive functionals of random
processes. Using the developed general technique, we derive uniform bounds on
the ${\mathbb{L}}_s$-norms of empirical and regression-type processes.
Usefulness of the obtained results is illustrated by application to the
processes appearing in kernel density estimation and in nonparametric
estimation of regression functions.
