Asymptotic Theory Of Finite Dimensional Normed Spaces Book

Part I: The concentration of measure phenomenon in the theory of normed spaces. Preliminaries; The isoperimetric inequality on Ssub(n-1) and some consequences; Finite dimensional normed spaces; Almost euclidean subspaces of a normed space; Almost euclidian subspaces of l_psubn spaces of general n-dimensional normed spaces and of quotient of n-dimensional spaces; Levy families; Martingales; Embedding l_psubm into l_1subn; Type and cotype of normed spaces, and some simple relations with geometrical properties; Additional applications of Levy families in the theory of finite dimensional normed spaces. Part II: Type and cotype of normed spaces. Ramsey's theorem with some applications to normed spaces; Krivine's theorem; The Maurey-Pisier theorem; The Rademacher projection; Projections on random euclidean subspaces of finite dimensional normed spaces. Appendices: