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arXiv · 1502.01487

On thin carpets for doubling measures

Changhao Chen·Shengyou Wen
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Abstract

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 Barański carpets are thin for doubling measures.

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Changhao Chen, Shengyou Wen. 2015-02-05. On thin carpets for doubling measures. https://arxiv.org/abs/1502.01487

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