Show simple item record

Files in this item

Thumbnail

Item metadata

dc.contributor.authorFalconer, Kenneth
dc.contributor.authorMattila, Pertti
dc.date.accessioned2017-01-06T15:30:11Z
dc.date.available2017-01-06T15:30:11Z
dc.date.issued2016
dc.identifier.citationFalconer , K & Mattila , P 2016 , ' Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes ' , Journal of Fractal Geometry , vol. 3 , no. 4 , pp. 319-329 . https://doi.org/10.4171/JFG/38en
dc.identifier.issn2308-1309
dc.identifier.otherPURE: 173352822
dc.identifier.otherPURE UUID: 75e7f90b-2bb6-4e46-8e19-30e221e8e77d
dc.identifier.otherArXiv: http://arxiv.org/abs/1503.01284v1
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055277
dc.identifier.otherWOS: 000392517900001
dc.identifier.urihttps://hdl.handle.net/10023/10058
dc.description.abstractWe present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional measure, has Hausdorff dimension min(1,s), i.e. the set of exceptional directions is independent of F. Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.
dc.format.extent10
dc.language.isoeng
dc.relation.ispartofJournal of Fractal Geometryen
dc.rights© 2016, European Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.ems-ph.org/journals / https://doi.org/10.4171/JFG/38en
dc.subjectProjection theoremsen
dc.subjectHausdorff dimensionen
dc.subjectLine setsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleStrong Marstrand theorems and dimensions of sets formed by subsets of hyperplanesen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.4171/JFG/38
dc.description.statusPeer revieweden
dc.identifier.urlhttp://arxiv.org/abs/1503.01284en
dc.identifier.urlhttp://www.ems-ph.org/doi/10.4171/JFG/38en


This item appears in the following Collection(s)

Show simple item record