The univariate conditions of Gnedenko characterizing domains of attraction for univariate extreme value distributions are generalized to higher dimensions. In addition, it is shown that random variables with a multivariate extreme value distribution are associated. Applications are given to a number of parametric families of joint distributions with given marginal distributions.
"Domains of Attraction of Multivariate Extreme Value Distributions." Ann. Probab. 11 (1) 168 - 177, February, 1983. https://doi.org/10.1214/aop/1176993666