Mixed volumes and related concepts
The concept of mixed volumes, which forms a central part of the Brunn–Minkowski theory of convex bodies, arises naturally if one combines the two fundamental concepts of Minkowski addition and volume. In this chapter, we introduce mixed volumes and the closely related mixed area measures, establish their fundamental properties and study some related notions.
5.1 Mixed volumes and mixed area measures
Of several possible approaches to mixed volumes, we choose the one using strongly isomorphic polytopes, and then approximation on the basis of Theorem 2.4.15. This has several advantages: it is particularly perspicuous and elementary, it allows us to introduce the mixed area measures in a parallel fashion and it ...