ASYMPTOTIC ESTIMATES FOR BEST AND STEPWISE APPROXIMATION OF CONVEX-BODIES .1.

This article contains asymptotic formulae as n --> infinity for the di stance of a smooth convex body and its best approximating polytopes wi th n facets or vertices, resp. the convex hull of the first n points o f a sequence in its boundary. Distance means distance in the sense of Banach-Mazur or Hausdorff.