Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability

We prove some criteria for (Formula presented.) -rectifiability of (Formula presented.) -dimensional subsets of (Formula presented.) in terms of suitable approximate tangent paraboloids. We also include the case where the existence of the tangent plane is not assumed a priori, measuring on dyadic scales how close the set is to a (Formula presented.) -plane. We then discuss the relation with similar criteria involving Peter Jones' (Formula presented.) -numbers, in particular proving that a sufficient condition for (Formula presented.) -rectifiability is the boundedness for small (Formula presented.) of (Formula presented.) for (Formula presented.) -a.e. (Formula presented.) and for some (Formula presented.).