  Both Marcinkiewicz-Zygmund strong laws of large numbers (MZ-SLLNs) and
ordinary strong laws of large numbers (SLLNs) for plug-in estimators of general
statistical functionals are derived. It is used that if a statistical
functional is "sufficiently regular", then a (MZ-) SLLN for the estimator of
the unknown distribution function yields a (MZ-) SLLN for the corresponding
plug-in estimator. It is in particular shown that many L-, V- and risk
functionals are "sufficiently regular", and that known results on the strong
convergence of the empirical process of \alpha-mixing random variables can be
improved. The presented approach does not only cover some known results but
also provides some new strong laws for plug-in estimators of particular
statistical functionals.
