Article ID Journal Published Year Pages File Type
5774803 Journal of Mathematical Analysis and Applications 2017 24 Pages PDF
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+−V−, where both V+ and V− are positive radial continuous valuations.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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