f-Divergence for convex bodies

  title={f-Divergence for convex bodies},
  author={Elisabeth M. Werner},
  • 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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