A remark on Myrberg initial data for Kleinian groups

For a general Kleinian (N + 1)-manifold, we consider the set of those initial data which give rise to trajectories reproducing the global canonical geodesic structure with arbitrary accuracy. We show that the positivity of the Patterson measure of this set is equivalent to the ergodicity of the geodesic flow on the manifold. This result allows us to generalize the Myrberg density theorem to Kleinian groups whose exponent of convergence delta exceeds N/2 and which are of delta-divergence type.