Villanueva Díez, Ignacio2023-06-182023-06-182016Villanueva Díez, I. «Radial Continuous Rotation Invariant Valuations on Star Bodies». Advances in Mathematics, vol. 291, marzo de 2016, pp. 961-81. DOI.org (Crossref), https://doi.org/10.1016/j.aim.2015.12.030.0001-870810.1016/j.aim.2015.12.030https://hdl.handle.net/20.500.14352/24365We characterize the positive radial continuous and rotation invariant valuations V defined on the star bodies of Rn as the applications on star bodies which admit an integral representation with respect to the Lebesgue measure. That is,V(K)=∫Sn−1θ(ρK)dm, where θ is a positive continuous function, ρK is the radial function associated to K and m is the Lebesgue measure on Sn−1. As a corollary, we obtain that every such valuation can be uniformly approximated on bounded sets by a linear combination of dual quermassintegrals.engjournal articlehttps//doi.org/10.1016/j.aim.2015.12.030http://www.sciencedirect.com/science/article/pii/S0001870816000335http://arxiv.org/abs/1503.06064restricted access517Convex geometryValuationsStar bodiesAnálisis matemático1202 Análisis y Análisis Funcional