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dc.contributor.authorFalconer, Kenneth
dc.contributor.authorJin, Xiong
dc.date.accessioned2014-09-30T09:01:02Z
dc.date.available2014-09-30T09:01:02Z
dc.date.issued2014-10
dc.identifier47500067
dc.identifier19b4a4ea-f758-4f28-a5c1-9f0095429aad
dc.identifier84908361087
dc.identifier000345834700004
dc.identifier.citationFalconer , K & Jin , X 2014 , ' Exact dimensionality and projections of random self-similar measures and sets ' , Journal of the London Mathematical Society , vol. 90 , no. 2 , pp. 388-412 . https://doi.org/10.1112/jlms/jdu031en
dc.identifier.issn0024-6107
dc.identifier.otherArXiv: http://arxiv.org/abs/1212.1345v2
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055246
dc.identifier.urihttps://hdl.handle.net/10023/5514
dc.description.abstractWe study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu's for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and fractal percolation, including new results on projections, C1-images and distance sets.
dc.format.extent25
dc.format.extent324101
dc.language.isoeng
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.subjectQA Mathematicsen
dc.subjectBDCen
dc.subject.lccQAen
dc.titleExact dimensionality and projections of random self-similar measures and setsen
dc.typeJournal articleen
dc.contributor.sponsorThe Royal Societyen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1112/jlms/jdu031
dc.description.statusPeer revieweden
dc.identifier.urlhttp://arxiv.org/abs/1212.1345en
dc.identifier.grantnumbern/aen


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