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On thin carpets for doubling measures

Authors: Changhao Chen and Shengyou Wen
Journal: Proc. Amer. Math. Soc. 147 (2019), 3439-3449
MSC (2010): Primary 28A80; Secondary 28A75
Published electronically: March 21, 2019
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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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Additional Information

Changhao Chen
Affiliation: Department of Mathematical Sciences, P.O. Box 3000, 90014 University of Oulu, Finland

Shengyou Wen
Affiliation: Department of Mathematics and Key Laboratory of Applied Mathematics of Hubei University, Wuhan 430062, People’s Republic of China

Keywords: Doubling measure, isotropic doubling, self-affine set
Received by editor(s): November 2, 2017
Received by editor(s) in revised form: June 6, 2018, and November 14, 2018
Published electronically: March 21, 2019
Additional Notes: This research was supported by the Vilho, Yrjö, and Kalle Väisälä Foundation and by the NSFC (grants No. 11871200, 11271114, and 11671189).
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2019 American Mathematical Society