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Additional Applications of Levy Families in the Theory of Finite Dimensional Normed Spaces

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1200)

Abstract

We saw in the previous chapters some applications of the concentration of measure phenomenon on S n . For example, we have proved in Chapters 4, 5 and 9 Dvoretzky’s Theorem and some of its generalizations. We have also seen applications of the same phenomenon and of some martingale techniques in the families {E 2 nn } n=1 and {Π n } n=1 (see e.g., Theorem 9.7 and most of Chapter 8). In this chapter we will see a somewhat different kind of applications using some other Levy families. Some of the examples will be described only briefly leaving most of the details to the reader.

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© Springer-Verlag Berlin Heidelberg 1986

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