ABSTRACT
In my paper To the theory o f mixed volumes o f convex bodies,2 I in troduced the concept of the area function F (H ,u ) of a convex body H . By definition, F ( H , u>) is the area of the set of points on the surface of H through which the supporting planes pass whose outward normals fall into the set u) on the unit sphere ft, if they are drawn from the center of the sphere. I also proved there that F (H ,u ) is a countably additive function of the set oj and that the mixed volume of the body H and a convex body L can be expressed by a Lebesgue-Stieltjes integral taken over the surface ft of the ball as
Here and in what follows, n always denotes the dimension of space, h a unit normal or (if necessary) a point on the sphere ft and L(h) the support function of the body L. The concept of mixed area function and its appli cations in the theory of mixed volumes are largely based on the proposition expressed by formula ( 1 ).
