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Radial continuous valuations on star bodies

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Villanueva, Ignacio and Tradacete Pérez, Pedro (2017) Radial continuous valuations on star bodies. Journal of Mathematical Analysis and Applications, 454 (2). pp. 995-1018. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X17304754


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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.


Item Type:Article
Uncontrolled Keywords:Convex geometry; Star bodie; Valuations
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:44060
Deposited On:24 Jul 2017 08:36
Last Modified:24 Jul 2017 10:42

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