f-Divergence for Convex Bodies

Abstract

We introduce f-divergence, a concept from information theory and statistics, for convex bodies in ℝn. We prove that f-divergences are SL(n) invariant valuations and we establish an affine isoperimetric inequality for these quantities. We show that generalized affine surface area and in particular the Lpaffine surface area from the LpBrunn Minkowski theory are special cases of f-divergences. © Springer Science+Business Media New York 2013.