A definition of the ordering of a multivariate sample--based on the isobar surfaces--is used in order to obtain limit laws for the extreme values of a multidimensional sample.

A continuous c.d.f. F(x), strictly increasing for x 0, is exponential if and only if Xj, n - Xi, n and Xj-i, n-i have identical distribution for some i, n, J = j1, j2, 1 [less-than-or-equals, slant] i j1 j2 [less-than-or-equals, slant] n, n [greater-or-equal, slanted] 3. A new proof of this...