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Exact dimensionality and projections of random self-similar measures and sets

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Author(s)

Kenneth Falconer, Xiong Jin

School/Research organisations

Abstract

We 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 Feng and Hu's result 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.
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Details

Original languageEnglish
Pages (from-to)388-412
Number of pages25
JournalJournal of the London Mathematical Society
Volume90
Issue number2
Early online date14 Jul 2014
DOIs
Publication statusPublished - Oct 2014

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