Mixed functionals of convex bodies (Q1580776)

In [NATO ASI Ser., Ser. C, Math. Phys. Sci. 440, 273-299 (1994; Zbl 0815.52003)], the author presented a formula expressing the mixed volume of polytopes in terms of volumes of lower-dimensional faces. Here, a similar representation is proved for the mixed functionals of translative integral geometry. In fact, both results are derived from a more general theorem, which deals with mixed functionals induced by a surjective linear mapping \(f:(\mathbb{R}^n)^k \to(\mathbb{R}^n)^r\).