The strong law of large numbers for k-means and best possible nets of Banach valued random variables

Abstract

Let B be a uniformly convex Banach space, X a B-valued random variable and k a given positive integer number. A random sample of X is substituted by the set of k elements which minimizes a criterion. We found conditions to assure that this set converges a.s., as the sample size increases, to the set of k-elements which minimizes the same criterion for X. © 1988 Springer-Verlag.