The strong law of large numbers for k-means and best possible nets of Banach valued random variables
type: Item
instance of: scholarly article
title: The strong law of large numbers for k-means and best possible nets of Banach valued random variables
zbMATH Open document ID: 0628.60010
DOI: 10.1007/BF00353875
publication date: 1988-01-01T00:00:00Z
review text: 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 \(X\).
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4022240
zbMATH Keywords: nets of Banach valued random variables
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: uniformly convex Banach space
author: Juan Antonio Cuesta
author: Carlos Matrán
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4022240