On the empirical process of multivariate, dependent random variables

A convergence theorem of Billingsley for the empirical process of stationary, real valued radom variables under a mixing condition is generalized to the k-dimensional and nonstationary case. Further a more general empirical process is treated, including the upper summation boundary as argument. Some applications are given to a Kolmogorov-Smirnov and a Cramér-von Mises type statistic.