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Finite type in measure sense for self-similar sets with overlaps

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Abstract

For self-similar sets with overlaps, we introduce a notion named the finite type in measure sense and reveal its intrinsic relationships with the weak separation condition and the generalized finite type.

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Acknowledgements

The authors thank Professor dejun Feng for helpful discussion.

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Authors and Affiliations

  1. Department of Mathematics, ShenZhen University, ShenZhen, 518000, People’s Republic of China

    Juan Deng

  2. Department of Mathematics, Tsinghua University, Beijing, 100084, People’s Republic of China

    Zhiying Wen

  3. Department of Mathematics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Lifeng Xi

  4. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Lifeng Xi

Authors
  1. Juan Deng
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Correspondence to Lifeng Xi.

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Supported by National Natural Science Foundation of China (Nos. 11831007, 11771226, 11871098, 11371329, 11301346) and K.C. Wong Magna Fund in Ningbo University.

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Deng, J., Wen, Z. & Xi, L. Finite type in measure sense for self-similar sets with overlaps. Math. Z. 298, 821–837 (2021). https://doi.org/10.1007/s00209-020-02632-3

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