  In the present paper we sketch the proof of the fact 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.
