Sets of independent vectors in spaces of indefinitely increasing dimension

We study a region of a space in which are concentrated independent observations of random vectors if the dimension of the space and the number of observations approaches infinity, and the distribution function of the components _k ⁱ of the observed vectors does not depend on n or m and satisfies the conditions: 1) it is continuous and symmetric: F(x) = 1-F(–x); 2) its tails are slowly varying functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 691–696, May, 1992.