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In the paper, it is proved that for any Ahlfors–David s-regular sets E and F in Euclidean spaces, there exist subsets E ⊂ E and F ′ ⊂ F such that dimH E = dimH F ′ = s and E, F ′ are quasi-Lipschitz equivalent.

Quasi-Lipschitz equivalence of subsets of Ahlfors-David regular sets