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Dynamics of the scenery flow and geometry of measures

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Käenmäki, A., Sahlsten, T., & Shmerkin, P. (2015). Dynamics of the scenery flow and geometry of measures. Proceedings of the London mathematical society, 110 (5), 1248-1280. doi:10.1112/plms/pdv003
Published in
Proceedings of the London mathematical society
Authors
Käenmäki, Antti |
Sahlsten, Tuomas |
Shmerkin, Pablo
Date
2015
Discipline
Matematiikka
Copyright
© London Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by London Mathematical Society.

 
We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.
Publisher
Oxford University Press; London Mathematical Society
ISSN Search the Publication Forum
0024-6115
Keywords
scenery flow geometry measures mathematics
DOI
10.1112/plms/pdv003
URI

http://urn.fi/URN:NBN:fi:jyu-201510213435

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