An application of a martingale inequality of dubins and freedman to the law of large numbers in Banach spaces
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.
KeywordsBanach Space Conditional Variance Iterate Logarithm Smooth Banach Space Smooth Space
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