# f-Divergence for convex bodies

@article{Werner2012fDivergenceFC,
title={f-Divergence for convex bodies},
author={Elisabeth M. Werner},
journal={ArXiv},
year={2012},
volume={abs/1205.3423}
}
• E. Werner
• Published 15 May 2012
• Mathematics
• ArXiv
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.
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