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The dimension of projections of self-affine sets and measures

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Kenneth John Falconer, Thomas Michael William Kempton

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Abstract

Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if μ is a Bernoulli measure on E with dimHμ = dimLμ, where dimH and dimL denote Hausdorff and Lyapunov dimensions, then the projection of μ in all but at most one direction has Hausdorff dimension min{dimHμ, 1}. We transfer this result to sets and show that many self-affine sets have projections of dimension min{dimHE, 1} in all but at most one direction

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Original languageEnglish
Pages (from-to)473-486
Number of pages17
JournalAnnales Academiae Scientiarum Fennicae-Mathematica
Volume42
DOIs
Publication statusPublished - 6 Feb 2017

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