The structure of extreme value distributions in in finite-dimensional space is well known. We characterize the domain of attraction of such extreme-value distributions in the framework of Giné Hahn and Vatan. We intend to use the result for statistical applications.
"On convergence toward an extreme value distribution in C[0,1]." Ann. Probab. 29 (1) 467 - 483, February 2001. https://doi.org/10.1214/aop/1008956340