  Two classes of measure-valued valuations on convex functions related to
Monge-Amp\`ere operators are investigated and classified. It is shown that the
space of all valuations with values in the space of complex Radon measures on
$\mathbb{R}^n$ that are locally determined, continuous, dually epi-translation
invariant as well as translation equivariant, is finite dimensional. Integral
representations of these valuations and a description in terms of mixed
Monge-Amp\`ere operators are established, as well as a characterization of
$\mathrm{SO}(n)$-equivariant valuations in terms of Hessian measures.
