The strong law of large numbers for k-means and best possible nets of Banach valued random variables
- Cite this article as:
- Cuesta, J.A. & Matran, C. Probab. Th. Rel. Fields (1988) 78: 523. doi:10.1007/BF00353875
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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.