This paper concerns the Lipschitz equivalence of dust‐like self‐similar sets with commensurable ratios. We obtain an algebraic criterion of Falconer–Marsh type to check whether such two self‐similar sets are Lipschitz equivalent, and prove that it is a sufficient and necessary condition.

中文翻译：

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类尘自相似集的Lipschitz等价的代数准则

本文关注具有可比比率的类尘埃相似自相似集的Lipschitz等价性。我们获得了Falconer-Marsh型的代数准则，以检查这两个自相似集是否与Lipschitz等价，并证明这是一个充分必要的条件。