  The purpose of this paper is to prove a weak convergence result for empirical
processes indexed in general classes of functions and with an underlying
$\alpha$-mixing sequence of random variables. In particular the uniformly
boundedness assumption on the function class, which is required in most of the
existing literature, is spared. Furthermore under strict stationarity a weak
convergence result for the sequential empirical process indexed in function
classes is obtained, as a direct consequence. Two examples in mathematical
statistics, that cannot be treated with existing results, are given as possible
applications.
