Dynamics of the scenery flow and geometry of measures

@article{Kaenmaki2015DynamicsOT,
  title={Dynamics of the scenery flow and geometry of measures},
  author={Antti Kaenmaki and Tuomas Sahlsten and Pablo Shmerkin},
  journal={Proceedings of The London Mathematical Society},
  year={2015},
  volume={110},
  pages={1248-1280}
}
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… Expand

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