RT Journal Article
T1 Continuous valuations on the space of Lipschitz on the sphere
A1 Colesanti, Andrea
A1 Pagnini, Daniele
A1 Tradacete Pérez, Pedro
A1 Villanueva Díez, Ignacio
AB 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.Contents
PB Elsevier
SN 0022-1236
YR 2020
FD 2020-11-30
LK https://hdl.handle.net/20.500.14352/7253
UL https://hdl.handle.net/20.500.14352/7253
LA eng
NO 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.
NO Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
NO Ministerio de Economía, Comercio y Empresa (España)
NO Comunidad de Madrid
NO Centro de Excelencia Severo Ochoa
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 8 abr 2025