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Lipschitz representations of subsets of the cube

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dc.contributor.authorMendelson, Shahar
dc.date.accessioned2016-03-15T23:29:52Z
dc.date.available2016-03-15T23:29:52Z
dc.date.issued2007-11-14
dc.date.updated2016-06-14T08:44:49Z
dc.description.abstractWe show that for any class of uniformly bounded functions H with a reasonable combinatorial dimension, the vast majority of small subsets of the n-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space.
dc.description.sponsorshipThe author was supported in part by an Australian Research council Discovery grant.en_AU
dc.identifier.issn0002-9939en_AU
dc.identifier.urihttp://hdl.handle.net/1885/100414
dc.publisherAmerican Mathematical Society
dc.rights© 2006 American Mathematical Society
dc.sourceProceedings of the American Mathematical Society
dc.titleLipschitz representations of subsets of the cube
dc.typeJournal article
local.bibliographicCitation.issue05en_AU
local.bibliographicCitation.lastpage1464en_AU
local.bibliographicCitation.startpage1455en_AU
local.contributor.affiliationMendelson, Shahar, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National Universityen_AU
local.contributor.authoruidu4011413en_AU
local.description.notesImported from ARIESen_AU
local.identifier.absfor010102en_AU
local.identifier.ariespublicationu3488905xPUB48en_AU
local.identifier.citationvolume135en_AU
local.identifier.doi10.1090/S0002-9939-06-08620-5en_AU
local.identifier.scopusID2-s2.0-55149119526
local.publisher.urlhttp://www.ams.org/journals/en_AU
local.type.statusPublished Versionen_AU

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