No abstract

No abstract

It is shown that if C is an n‐dimensional convex body then there is an affine image C˜ of C for which |∂C˜|/|C˜(n−1)/n is no larger than the corresponding expression for a regular n‐dimensional ‘tetrahedron’. It is also shown that among n‐dimensional subspaces of Lp (for eachp∈[1,∞]), lpn has maximal volume ratio.

Abstract. It is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately Gaussian. Several quite broad classes of bodies are shown to satisfy the condition.