Principal values for the Cauchy integral and rectifiability

We give a geometric characterization of those positive finite measures mu on C with the upper density lim sup(r --> 0) mu({xi:\xi-z\less than or equal to r}) finite at mu-almost every z is an element of C, such that the principal value of the Cauchy integral of mu, [GRAPHICS] exists for mu-almost all z is an element of C. This characterization is given in terms of the curvature of the measure mu. In particular, we get that for E subset of C, H-1-measurable (where H-1 is the Hausdorff 1-dimensional measure) with 0 < H-1 (E) < infinity, if the principal value of the Cauchy integral of H-\E(1) exists H-1-almost everywhere in E, then E is rectifiable.