  We show the David-Jerison construction of big pieces of Lipschitz graphs
inside a corkscrew domain does not require its surface measure be upper Ahlfors
regular. Thus we can study absolute continuity of harmonic measure and surface
measure on NTA domains of locally finite perimeter using Lipschitz
approximations. A partial analogue of the F. and M. Riesz Theorem for simply
connected planar domains is obtained for NTA domains in space. As a consequence
every Wolff snowflake has infinite surface measure.
