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An application of a martingale inequality of dubins and freedman to the law of large numbers in Banach spaces

  • Bernard Heinkel
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1193)

Abstract

In a real, separable, p-uniformly smooth Banach space the law of large numbers in the Prohorov setting is studied by a method depending on a result of Dubins and Freedman which compares the distribution of a real valued martingale with the one of the associated conditional variances. Some laws of large numbers of Kolmogorov-Brunk type are also given.

Keywords

Banach Space Conditional Variance Iterate Logarithm Smooth Banach Space Smooth Space 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Bernard Heinkel
    • 1
  1. 1.Département de MathématiqueStrasbourg CédexFrance

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