  We prove pointwise and maximal ergodic theorems for probability measure
preserving (p.m.p.) actions of any countable group, provided it admits an
essentially free, weakly mixing amenable action of stable type $III_1$. We show
that this class contains all irreducible lattices in connected semisimple Lie
groups without compact factors. We also establish similar results when the
stable type is $III_\lambda$, $0 < \lambda < 1$, under a suitable hypothesis.
  Our approach is based on the following two principles. First, we show that it
is possible to generalize the ergodic theory of p.m.p. actions of amenable
groups to include p.m.p. amenable equivalence relations. Second, we show that
it is possible to reduce the proof of ergodic theorems for p.m.p. actions of a
general group to the proof of ergodic theorems in an associated p.m.p. amenable
equivalence relation, provided the group admits an amenable action with the
properties stated above.
