  We construct quasiconformal mappings in Euclidean spaces by integration of a
discontinuous kernel against doubling measures with suitable decay. The
differentials of mappings that arise in this way satisfy an isotropic form of
the doubling condition. We prove that this isotropic doubling condition is
satisfied by the distance functions of certain fractal sets. Finally, we
construct an isotropic doubling measure that is not absolutely continuous with
respect to the Lebesgue measure.
