Continuous valuations on the space of Lipschitz on the sphere
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2020
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Elsevier
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Colesanti, A., Pagnini, D., Tradacete Pérez, P. et al. «Continuous Valuations on the Space of Lipschitz Functions on the Sphere». Journal of Functional Analysis, vol. 280, n.o 4, febrero de 2021, p. 108873. DOI.org (Crossref), https://doi.org/10.1016/j.jfa.2020.108873.
Abstract
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere Sn−1. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect to the Lipschitz norm. This fact, in combination with measure theoretical arguments, will yield an integral representation for continuous and rotation invariant valuations on the space of Lipschitz functions over the 1-dimensional sphere.
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