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Ledrappier-Young formula and exact dimensionality of self-affine measures

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Bárány, B., & Käenmäki, A. (2017). Ledrappier-Young formula and exact dimensionality of self-affine measures. Advances in Mathematics, 318(1), 88-129. https://doi.org/10.1016/j.aim.2017.07.015
Published in
Advances in Mathematics
Authors
Bárány, Balázs |
Käenmäki, Antti
Date
2017
Discipline
MatematiikkaMathematics
Copyright
© 2017 Elsevier Inc. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.

 
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.
Publisher
Elsevier
ISSN Search the Publication Forum
0001-8708
Keywords
self-affine set self-affine measure hausdorff dimension local dimension
DOI
https://doi.org/10.1016/j.aim.2017.07.015
URI

http://urn.fi/URN:NBN:fi:jyu-201708023396

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/27142678

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