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Measure-valued valuations on star bodies
Jorge S. Ibáñez-Marcos, Monika Ludwig, Pedro Tradacete +1
A complete classification of weak~continuous, measure-valued valuations is established on star bodies in . Consequences are an integral representation of rotation equivar…
Non-continuous valuations on convex bodies and a new characterization of volume
Jorge S. Ibáñez Marcos, Pedro Tradacete, Ignacio Villanueva
This paper investigates the use of automatic continuity techniques in the context of valuations on convex bodies. We first provide an automatic continuity theorem for valuations re…
Continuous valuations on the space of Lipschitz functions on the sphere
Andrea Colesanti, Daniele Pagnini, Pedro Tradacete +1
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere . After introducing an appropriate notion of convergence, we show that c…
Continuity and representation of valuations on star bodies
Pedro Tradacete, Ignacio Villanueva
It is shown that every continuous valuation defined on the -dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the…