On samples of independent random vectors in spaces of infinitely increasing dimension

Abstract

We study the asymptotic behavior of a set of random vectors ξi, i = 1,..., m, whose coordinates are independent and identically distributed in a space of infinitely increasing dimension. We investigate the asymptotics of the distribution of the random vectors, the consistency of the sets Mm(n) = ξ1,..., ξm and Xnλ = x ∈ Xn: ρ(x) ≤ λn, and the mutual location of pairs of vectors.