On thin carpets for doubling measures

@article{Chen2015OnTC,
  title={On thin carpets for doubling measures},
  author={Changhao Chen and Sheng-you Wen},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
  • Changhao Chen, Sheng-you Wen
  • Published 2015
  • Mathematics
  • arXiv: Classical Analysis and ODEs
We study subsets of $\R^{d}$ which are thin for doubling measures or isotropic doubling measures. We show that any subset of $\R^{d}$ with Hausdorff dimension less than or equal to $d-1$ is thin for isotropic doubling measures. We also prove that a self-affine set that satisfies $OSCH$ (open set condition with holes) is thin for isotropic doubling measures. For doubling measures, we prove that Bara\'nski carpets are thin for doubling measures. 
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