Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774803 | Journal of Mathematical Analysis and Applications | 2017 | 24 Pages |
Abstract
We show that a radial continuous valuation defined on the n-dimensional star bodies extends uniquely to a continuous valuation on the n-dimensional bounded star sets. Moreover, we provide an integral representation of every such valuation, in terms of the radial function, which is valid on the dense subset of the simple Borel star sets. Along the way, we also show that every radial continuous valuation defined on the n-dimensional star bodies can be decomposed as a sum V=V+âVâ, where both V+ and Vâ are positive radial continuous valuations.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Pedro Tradacete, Ignacio Villanueva,