“…The cone-volume measure for convex bodies has been studied extensively over the last few years in many different contexts, see, e.g., [4,5,10,11,12,23,25,27,28,29,30,31,34,35,39,40,41,42,43,44,47,51,55,56]. One very important property of the cone-volume measure -and which makes it so essential -is its SL(n)-invariance, or simply called affine invariance.…”