  In this paper we develop a theory of Patterson--Sullivan measures associated
to coarse cocycles of convergence groups. This framework includes
Patterson-Sullivan measures associated to the Busemann cocycle on the geodesic
boundary of a Gromov hyperbolic metric spaces and Patterson-Sullivan measures
on flag manifolds associated to Anosov (or more general transverse) subgroups
of semisimple Lie groups, as well as more examples. Under some natural
geometric assumptions on the coarse cocycle, we prove existence, uniqueness,
and ergodicity results.
