  We prove an inequality concerning isometries of a Gromov hyperbolic metric
space, which does not require the space to be proper or geodesic. It involves
the joint stable length, a hyperbolic version of the joint spectral radius, and
shows that sets of isometries behave like sets of $2 \times 2$ real matrices.
Among the consequences of the inequality, we obtain the continuity of the joint
stable length and an analogue of Berger-Wang theorem.
