On thin carpets for doubling measures

Chen, Changhao; Wen, Shengyou

doi:10.1090/proc/14493

On thin carpets for doubling measures
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by Changhao Chen and Shengyou Wen PDF

Proc. Amer. Math. Soc. 147 (2019), 3439-3449 Request permission

Abstract:

We study thin sets for doubling or isotropic doubling measures in $\mathbb {R}^{d}$. In our results we prove that the self-affine sets satisfying the open set condition with holes are thin for isotropic doubling measures and among them Barański carpets are thin for doubling measures.

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