  We characterise the big pieces of Lipschitz graphs property in terms of
projections. Roughly speaking, we prove that if a large subset of an
$n$-Ahlfors-David regular set $E \subset \mathbb{R}^d$ has plenty of
projections in $L^{2}$, then a large part of $E$ is contained in a single
Lipschitz graph. This is closely related to a question of G. David and S.
Semmes.
