 Milman's theorem states that one can replace one of the bodies by its image under a properly chosen volume-preserving linear map so that the left-hand side of the Brunn–Minkowski inequality is bounded by a constant multiple of the right-hand side.The result is one of the main structural theorems in the local theory of Banach spaces.There is a constant "C", independent of "n", such that for any two centrally symmetric convex bodies "K" and "L" in R"n", there are volume-preserving linear maps "φ" and "ψ" from R"n" to itself such that for any real numbers "s", "t" > 0

One of the maps may be chosen to be the identity.