Probability Theory and Related Fields

, Volume 78, Issue 4, pp 523–534 | Cite as

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

  • J. A. Cuesta
  • C. Matran
Article

Summary

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.

Keywords

Banach Space Positive Integer Assure Random Sample Stochastic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. A. Cuesta
    • 1
    • 2
  • C. Matran
    • 1
    • 2
  1. 1.Department of StatisticsUniversity of SantanderSantanderSpain
  2. 2.Department of StatisticsUniversity of ValladolidValladolidSpain

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