  All non-negative, continuous, $\operatorname{SL}(n)$ and translation
invariant valuations on the space of super-coercive, convex functions on
$\mathbb{R}^n$ are classified. Furthermore, using the invariance of the
function space under the Legendre transform, a classification of non-negative,
continuous, $\operatorname{SL}(n)$ and dually translation invariant valuations
is obtained. In both cases, different functional analogs of the Euler
characteristic, volume and polar volume are characterized.
