The maximum domain of attraction of multivariate extreme value distributions is small

Abstract

Consider the set of Borel probability measures on ${\mathbf{R}}^k$ and endow it with the topology of weak convergence. We show that the subset of all probability measures which belong to the domain of attraction of some multivariate extreme value distributions is dense and of the first Baire category. In addition, the analogue result holds in the context of free probability theory.