The Hadwiger theorem on convex functions. I

Andrea Colesanti, Monika Ludwig, Fabian Mussnig

Published 2020-09-08Version 1

A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb R}^n$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.