Weak approximations of the empirical process when parameters are estimated -- On the Erdös-Rényi increments and the P. Lévy modulus of continuity of a kiefer process -- Kolmogorov-smirnov tests when parameters are estimated -- On uniform convergence of measures with applications to uniform convergence of empirical distributions -- An alternative approach to glivenko-cantelli theorems -- Weak convergence under contiguous alternatives of the empirical process when parameters are estimated: The Dk approach -- Almost sure invariance principles for empirical distribution functions of weakly dependent random variables -- Three theorems of multivariate empirical process -- Weak convergence to stable laws by means of a weak invariance principle -- A necessary condition for the convergence of the isotrope discrepancy -- Two examples concerning uniform convergence of measures w.r.t. balls in Banach spaces.