Continuity and representation of valuations on star bodies

• Published in: Advances in mathematics (New York. 1965) Vol. 329; pp. 361 - 391
• Main Authors: Tradacete, Pedro, Villanueva, Ignacio
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 30.04.2018
• Subjects: Star bodies; Star sets; Valuations; Star bodies; Star sets; 52A30; 52B45; Valuations

It is shown that every continuous valuation defined on n-dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize continuous valuatio...