The Volume of Convex Bodies and Banach Space Geometry

Now in paperback, this popular book gives a self-contained presentation of a number of recent results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory, and the local theory of Banach spaces. The first part of the book presents self-contained proofs of the quotient of the subspace theorem,...