On thin carpets for doubling measures

2015/02/05 by Chen, Changhao, Wen, Shengyou
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.01487

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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