%0 Journal Article
%A Villanueva, Ignacio
%T Radial continuous rotation invariant valuations on star bodies
%D 2016
%@ 0001-8708
%U https://hdl.handle.net/20.500.14352/24365
%X We 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.
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