Inequalities for the product of the volumes of a partition determined in a convex body by a surface

A generalization is given of the work of J. Bokowski 1] referring to the product of the volumes of the two parts into which a convex body is divided by a plane. The proof uses formulas of Integral Geometry and a conjecture of L. A. Santaló 2], and holds for the two parts determined by any (n?1)-dimensional surface in the euclideann-space and for dimensionsn=2, 3 in the hyperbolic space.