When is the product of the d.f.'s H1(·), ···, Hm(·) attracted to an extreme value law φ(x)? We associate with each Hi(·) its A-function Hi(x) is attracted to φ(x) if each Hi(x) is in the domain of attraction of φ(x) and Ai(z) ~ Aj(z), 1 ≦ i, j ≦ m. Equivalence of A-functions determines an equivalence relation which partitions the domain of attraction of φ(x)into one or more convex sets. These sets fail to be closed under passages to the limit (complete convergence).