  We show that, in long time, quantum trajectories select an invariant subspace
of the Hilbert space of the system being indirectly measured. This selection is
shown to be exponentially fast in an almost sure sense and in average. This
result generalizes a known result for non demolition measurements to arbitrary
repeated indirect measurements. Our proofs are based on the introduction of a
deformation of the original instrument to an equivalent one with a unique
invariant state.
