Titlebook: Probability in Banach Spaces; Isoperimetry and Pro Michel Ledoux,Michel Talagrand Book 1991 Springer-Verlag Berlin Heidelberg 1991 Banach S

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NotationHere, we present some general and basic notation which we have . to keep coherently throughout the book.

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Introductions probabilistic sources may be found in the study of regularity of random processes (especially Gaussian processes) and Banach space valued random variables and their limiting properties, whose functional developments revealed and tied up strong and fruitful connections with classical Banach spaces and their geometry.

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Gaussian Random Variablesconsidered as one of the fundamental topics of the theory since it inspires many other parts of the field both in the results themselves and in the techniques of investigation. Historically, the developments also followed this line of progress.

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The Strong Law of Large Numbersdent Banach space valued random variables. In this study, the isoperimetric approach of Section 6.3 demonstrates its efficiency. We only investigate extensions to vector valued random variables of some of the classical limit theorems such as the laws of large numbers of Kolmogorov and Prokhorov.

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https://doi.org/10.1007/978-3-642-20212-4Banach Space; Fourier series; Law of large numbers; Random variable; differential equation; entropy; law o