## Asymptotic Theory of Finite Dimensional Normed Spaces, Issue 1200 |

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### Contents

The concentration of measure phenomenon in the theory of normed spaces 1 Preliminaries | 1 |

The isoperimetric inequality on Sn_i and some consequences | 5 |

Finite dimensional normed spaces preliminaries | 9 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

5n_i absolute constant applications assume Banach space block finitely representable Chapter compact convex corollary define denote dimensional normed spaces dimensional subspace Dvoretzky's Theorem Edited ellipsoid estimate euclidean norm Euclidean structure example exists a constant family with constants finite dimensional normed finite sequences follows gaussian given Haar measure hypersurface implies interior normal invariant isometric isoperimetric inequality Kahane's inequality Lemma linear Lipschitz map F martingale mean curvature median metric space n-dimensional normal Levy family normalized Haar measure Note operator orthogonal orthonormal Pisier probability space Proceedings projection proof of Theorem Proposition prove Rademacher functions radius Ramsey's Theorem random variables REMARK resp Riemannian manifold Riemannian metric satisfies scalars semigroup sphere subset subspace symmetric p-stable tangent Theorem 4.2 Theory triangle inequality type and cotype unit ball unit vector basis volume zero