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

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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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© 1986 Springer-Verlag

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Heinkel, B. (1986). An application of a martingale inequality of dubins and freedman to the law of large numbers in Banach spaces. In: Fernique, X., Heinkel, B., Meyer, PA., Marcus, M.B. (eds) Geometrical and Statistical Aspects of Probability in Banach Spaces. Lecture Notes in Mathematics, vol 1193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077098

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  • DOI: https://doi.org/10.1007/BFb0077098

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16487-6

  • Online ISBN: 978-3-540-39826-4

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