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In this paper, we consider the approximation problem on the volume of a convex body K in Rn by those of its radial mean bodies RpK. Specifically, we establish the identity lim p→∞ p log p (1− 2−n |Rp(K)| |K| ) = n(n+ 1) 2 , when K is an ellipsoid in Rn. c ©2016 All rights reserved.

On the approximation of a convex body by its radial mean bodies