We show that a statistical functional is asymptotically normal if it induces a Hadamard differentiable functional defined on the space D[0, 1]p. This work involves p-dimensional empirical processes. As an example we illustrate the use of the von Mises method in proving the asymptotic normality...

Weak invariance principles for certain continuous time parameter stochastic processes (including martingales and reverse martingales) are considered. Weak convergence in the sup-norm metric is also studied.