Abstract
Let F be a distribution function (d.f.) on Rd, d >_ 1. Suppose there exist norming constants an (i) > 0, bn(i) are real, 1 _ 1, and a d.f. K on Rd with ondegenerate univariate marginals such that (1.1) lim Fn(an(i)xi / bn(i), 1 <_ i <_ d) K(x), n.--400 x (xl,..., Xd) E C(K), where C(K) is the set of all continuity points of K. We call K a max stable d.f. under linear normalization or simply l-max stable d.f. In the univariate case it is well known that an l-max stable d.f. can be only one of the three types of extreme value d.f.’s of Gnedenko, namely,
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