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This note is intended to be a supplement to the bi-Lipschitz decomposition ofLipschitz maps shown in [Sch]. We show that in the case of 1-Ahlfors-regularsets, the condition of having `Big Pieces of bi-Lipschitz Images' (BPBI) isequivalent to a Carleson condition.

Big-Pieces-of-Lipschitz-Images Implies a Sufficient Carleson Estimate in a Metric Space