Measure-valued valuations on star bodies

Jorge S. Ibáñez-Marcos; Monika Ludwig; Pedro Tradacete; Ignacio Villanueva

Measure-valued valuations on star bodies

Metric Geometry 2026-06-29 v1

Authors: Jorge S. Ibáñez-Marcos , Monika Ludwig , Pedro Tradacete , Ignacio Villanueva

Abstract

A complete classification of weak $^*$ ~continuous, measure-valued valuations is established on star bodies in $\R^n$ . Consequences are an integral representation of rotation equivariant, measure-valued valuations and a characterization of dual area measures.

Cite

@article{arxiv.2606.30538,
  title  = {Measure-valued valuations on star bodies},
  author = {Jorge S. Ibáñez-Marcos and Monika Ludwig and Pedro Tradacete and Ignacio Villanueva},
  journal= {arXiv preprint arXiv:2606.30538},
  year   = {2026}
}

Comments

34 pages