Abstract
In Rao et al. (Comptes Rendus Acad Sci Paris Ser I(342):191–196, 2006), Rao–Ruan–Xi solved an open question posed by David and Semmes and gave a complete Lipschitz classification of self-similar sets on mathbb R with touching structure. In this short note, by applying a matrix rearrangeable condition introduced in Luo (J Lond Math Soc 99(2):428–446, 2019), we generalize their result onto the self-similar sets with overlapping structure.
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