  In the space of marked group, we suppose that a sequence $(G_i, X_i)$
converges to $(G,X)$, where $G$ is finitely presented. We obtain an inequality
which connects Dehn functions of $G_i$s and $G$. As a result, we show that if a
sequence $(K, X_i)$ converges to a hyperbolic marked group, then $K$ is already
hyperbolic.
