Radial continuous valuations on star bodies

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:454

Article

Tradacete, Pedro¹  Villanueva, Ignacio² 

[1] Univ Carlos III Madrid, Math Dept, Leganes 28911, Madrid, Spain

[2] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat, IMI, E-28040 Madrid, Spain

关键词: Convex geometry;    Star bodies;    Valuations;   

DOI  :  10.1016/j.jmaa.2017.05.026

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free