The strong law of large numbers for k-means and best possible nets of Banach valued random variables (Q1093233)

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 assurethat this set converges a.s., as the sample size increases, to the set of \(k\)-elements which minimizes the same criterion for \(X\).