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arXiv · 1908.10724

A homogeneous decomposition theorem for valuations on convex functions

A. Colesanti·M. Ludwig·F. Mussnig
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Abstract

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.

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A. Colesanti, M. Ludwig, F. Mussnig. 2019-08-28. A homogeneous decomposition theorem for valuations on convex functions. https://doi.org/10.1016/j.jfa.2020.108573

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