1. For a proof of this theorem, which is due to Minkowski, see, for example, W. Blaschke, Kreis und Kugel, § 17, 56–59, Leipzig 1916. — However we shall not need the theorem in this generality since, for the very simple convex bodies we shall consider, the existence of a content is obvious from elementary geometry or from familiar theorems of integral calculus.
2. In place of the proof due to Minkowski, which was presented in the first (German) edition of this book, we give here a much simpler proof, which in its basic outline goes back to Blichfeldt and in its details also to Hlawka.
3. H. F. Blichfeldt, Note on the discriminant of an algebraic field. Monatsh. Math. Phys. 48, 531–533 (1939).
4. C. A. Rogers, The product of n real homogeneous linear forms. Acta Math. 82, 185–208 (1950).
5. C. A. Rogers, The product of n homogeneous forms. J. London Math. Soc. 24, 31–39 (1949).