Entropy methods in asymptotic convex geometry

We extend to the general, not necessarily centrally symmetric setting a num ber of basic results of Local Theory which were known before for centrally symmetric bodies and were using very essentially the symmetry in their proo fs. The main additional tool is a study of volume behavior around the centr oid of the body. (C) 1999 Academie des Sciences / Editions scientifiques et medicales Elsevier SAS.