Abstract
It is proved that “most” convex bodies in IEd touch the boundaries of their minimal circumscribed and their maximal inscribed ellipsoids in preciselyd(d+3)/2 points. A version of the former result shows that for “most” compact sets in IEd the corresponding optimal designs, i.e. probability measures with a certain extremal property, are concentrated ond(d+1)/2 points.
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Gruber, P.M. Minimal ellipsoids and their duals. Rend. Circ. Mat. Palermo 37, 35–64 (1988). https://doi.org/10.1007/BF02844267
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DOI: https://doi.org/10.1007/BF02844267