The Hadwiger theorem on convex functions, IV: The Klain approach
Functional Analysis
2023-01-02 v2 Metric Geometry
Abstract
New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domains is proved, and its connection to the Abel transform is explained.
Keywords
Cite
@article{arxiv.2201.11565,
title = {The Hadwiger theorem on convex functions, IV: The Klain approach},
author = {Andrea Colesanti and Monika Ludwig and Fabian Mussnig},
journal= {arXiv preprint arXiv:2201.11565},
year = {2023}
}