Remark 13.5.6.label

1. (1)

   $E^{o}\supf C^{o}\supf \frac{1}{\sqrt{n}}E^{o}$

2. (2)

   $d_{BM}(K,B_{2}^{n})\leq \sqrt{n}$

3. (3)

   $d_{BM}(K,L)\leq d_{BM}(K,B_{2}^{n})d_{BM}(L,B_{2}^{n})\leq \sqrt{n}\sqrt{n}= n$

4. (4)

   If $C$ is a convex body then $\exists!$ ellipsoid of maximal volume included in $C$. Moreover $x_{0}+E\suf C\suf x_{0}+n E$