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Just enjoy!IntroductionIn this book, we present a solid exposition of the results explaining the interrelations existing between the metric geometry of Banach spaces and proba theory of vectors with values in those spaces. Particularly are studied martingales and random series of independant vectors.Chapter one introduces the simple geometric and probabilistic ideas of Banach spaces. Chapter two concentrates on the geometric concept of dentability and provides an exposition of some results. The conception of dentability seems to be extremely natural in the context of martingales despite the fact that it had been originally introducedin a study of the Radon-Nikodym theorem in Banach spaces. The chapter ends with an exposition of the concept of sub-martingales with values in Banach lattices and therefore the connected problems with the lattice bounded operators.Chapter three studies 2 classical ideas of metric geometric in Banach spaces, which are the uniform smoothness and the uniform convexity. It is shown that some of the results found earlier by the author for sums of independant random vectors in those Banach spaces push over to the additional general situation of martingales, hence give a whole characterization of these geometric properties within the martingales.
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Keywords : maths, banach spaces, martingales, geometry, english ebooks
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