Continuous valuations on the space of Lipschitz on the sphere

dc.contributor.authorColesanti, Andrea
dc.contributor.authorPagnini, Daniele
dc.contributor.authorTradacete Pérez, Pedro
dc.contributor.authorVillanueva, Ignacio
dc.description.abstractWe 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
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)/FEDER
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)
dc.description.sponsorshipComunidad de Madrid
dc.description.sponsorshipCentro de Excelencia Severo Ochoa
dc.description.sponsorshipUniversidad Complutense de Madrid
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dc.journal.titleJournal of functional analysis
dc.relation.projectIDQUITEMAD+-CM (S2013/ICE-2801)
dc.relation.projectID(SEV-2015-0554; 20205CEX001)
dc.relation.projectIDUCM (910346)
dc.rights.accessRightsopen access
dc.subject.keywordGeometric valuation Theory
dc.subject.keywordLipschitz functions
dc.subject.keywordIntegral representation
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleContinuous valuations on the space of Lipschitz on the sphere
dc.typejournal article
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