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

In this paper, we consider the approximation problem on the volume of a convex body K in R n by those of its radial mean bodies R p K : Specifically, we establish the identity limp→∞PlogP(1−2−n|RP(K)||K|)=n(n+1)2; when K is an ellipsoid in Rn.