  In the present paper we prove that for any open connected set
$\Omega\subset{\mathbb R}^{n+1}$, $n\geq 1$, and any $E\subset \partial\Omega$
with $0<{\mathcal H}^n(E)<\infty$ absolute continuity of the harmonic measure
$\omega$ with respect to the Hausdorff measure on $E$ implies that $\omega|_E$
is rectifiable.
