An Inequality between the parts into which a convex body is divided by a plane section

Abstract

A new proof is given of an inequality of ]. Bokowski and E. Sperner, referring to the product of the volume of the two parts into which a convex body is divided by a plane. The proof, which is given for dimensions n = 2,1 uses known formulas of Integral Geometry and is generalized to convex bodies of the elliptic and hyperbolic spaces