f-Divergence for convex bodies
Functional Analysis
2012-05-16 v1 Information Theory
math.IT
Abstract
We introduce f-divergence, a concept from information theory and statistics, for convex bodies in R^n. 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 L_p affine surface area from the L_p Brunn Minkowski theory are special cases of f-divergences.
Cite
@article{arxiv.1205.3423,
title = {f-Divergence for convex bodies},
author = {Elisabeth M. Werner},
journal= {arXiv preprint arXiv:1205.3423},
year = {2012}
}