Hadamard Differentiability on D[0,1]p

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 of Spearman′s rank correlation coefficient.