A homogeneous decomposition theorem for valuations on convex functions

摘要

The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree n are classified. By duality, corresponding results are obtained for valuations on finite-valued convex functions. (C) 2020 Elsevier Inc. All rights reserved.