  In complex dynamics, we construct a so-called nice set (one for which the
first return map is Markov) around any point which is in the Julia set but not
in the post-singular set, adapting a construction of Juan Rivera-Letelier. This
simplifies the study of absolutely continuous invariant measures. We prove a
converse to a recent theorem of Kotus and Swiatek, so for a certain class of
meromorphic maps the absolutely continuous invariant measure is finite if and
only if an integrability condition is satisfied.
