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dc.contributor.authorFalconer, Kenneth
dc.contributor.authorJin, Xiong
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 .
dc.identifier.otherPURE: 47500067
dc.identifier.otherPURE UUID: 19b4a4ea-f758-4f28-a5c1-9f0095429aad
dc.identifier.otherScopus: 84908361087
dc.identifier.otherORCID: /0000-0001-8823-0406/work/58055246
dc.identifier.otherWOS: 000345834700004
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.relation.ispartofJournal of the London Mathematical Societyen
dc.rights© 2014. London Mathematical Society. This is the accepted version before publication of the following article: Exact dimensionality and projections of random self-similar measures and sets Falconer, K. & Jin, X. 2014 In : Journal of the London Mathematical Society. 25 p., which has been published in final form at
dc.subjectQA Mathematicsen
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.description.statusPeer revieweden

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