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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