  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.
