In this paper we study sets on rectifiable curves removable for Hardy spaces of analytic functions on general domains. With the methods used it seems natural to distinguish between three different classes of rectifiable curves: chord-arc curves, curves of bounded rotation and curves with Dini continuous tangents. We give results both for sets on rectifiable Jordan curves and for sets on rectifiable curves which intersect. Among the results we prove that if K is a set lying on a rectifiable chord-arc curve, then there exists p < ∞ such that K is removable for H_p if and only if the generalized length of K is 0. Furthermore, if the curve is also of bounded rotation, then p can be arbitrarily chosen greater than 1.
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