  If $A$ and $B$ are two bounded sets of reals, Ruzsa proved a precise lower
bound of the measure of the sumset $A+B$ involving the ratio
$\lambda(A)/\lambda(B)$. De Roton established a structural result about the
critical sets of this lower bound. Here, we prove a generalization of de
Roton's work by establishing a result in a neighborhood of the case of
equality.
