Villanueva Díez, IgnacioTradacete Pérez, Pedro2023-06-172023-06-172017Tradacete Pérez, P. & Villanueva Díez, I. «Radial Continuous Valuations on Star Bodies». Journal of Mathematical Analysis and Applications, vol. 454, n.o 2, octubre de 2017, pp. 995-1018. DOI.org (Crossref), https://doi.org/10.1016/j.jmaa.2017.05.026.0022-247X10.1016/j.jmaa.2017.05.026https://hdl.handle.net/20.500.14352/17964We 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.engjournal articlehttps//doi.org/10.1016/j.jmaa.2017.05.026http://www.sciencedirect.com/science/article/pii/S0022247X17304754restricted access517.5Convex geometryStar bodieValuationsAnálisis funcional y teoría de operadores