Limit properties for multivariate extreme values in sequences of independent, non-identically distributed random vectors

Any multivariate distribution can occur as the limit of extreme values in a sequence of independent, non-identically distributed random vectors. Under a reasonable uniform negligibility condition the class of such limit distribution can be totally characterized, which extends the known univariate results. In addition, some results on the dependence structure of a possible limit law are given, as for instance the independence, the positive lower orthant dependence or the association.