How to use the functional empirical process for deriving asymptotic laws for functions of the sample

The functional empirical process is a very powerful tool for deriving asymptotic laws for almost any kind of statistics whenever we know how to express them into functions of the sample. Since this method seems to be applied more and more in the very recent future, this paper is intended to provide a complete but short description and justification of the method and to illustrate it with a non-trivial example using bivariate data. It may also serve for citation without repeating the arguments.