  The notion of a valuation on convex bodies is very classical. The notion of a
valuation on a class of functions was recently introduced and studied by M.
Ludwig and others. We study an explicit relation between continuous valuations
on convex functions which are invariant under adding arbitrary linear
functionals, and translations invariant continuous valuations on convex bodies.
More precisely, we construct a natural linear map from the former space to the
latter and prove that it has dense image and infinite dimensional kernel. The
proof uses the author's irreducibility theorem and few properties of the real
Monge-Ampere operators due to A.D. Alexandrov and Z. Blocki. Fur- thermore we
show how to use complex, quaternionic, and octonionic Monge-Ampere operators to
construct more examples of continuous valuations on convex functions in an
analogous way.
