A note on the covergence of bivariate extreme order statistics

In this note an interesting fact is proved that, for any vector of bivariate extreme order statistics there exists (at least) a sequence of vectors of real numbers for which the distrihution function (d.f.) of this vector converges to a nondegenerate limit if and only if its marginals converge to nondegenerate limits. Moreover, the limit splits into the product of the limit: marginals if the bivariate d.f., from which the order statistics are drawn, is of negative quadrant dependent random variables (r.v., s)