2009/12/25 by Lewis Bowen, Bowen, Lewis, Amos Nevo +1
Mathematics · #37A15 #37A30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A15 #msc:37A30
paper · pdf · doi:10.48550/arxiv.0912.4953
In the second version one section was added, proving the pointwise ergodic theorems in L(1) for an amenable equivalence relation with finite invariant measure which posseses an asymptotically invariant sequence satisfying the doubling condition. This is a more abstract formulation of the argument used in the first version, and applies more broadly
arxiv created 2010/09/02 · arxiv updated 2010/09/03
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering and asymptotic invariance arguments used in the ergodic theory of amenable groups. We use this approach to generalize the existing maximal and pointwise ergodic theorems for free group actions to a large class of geometric averages which were not accessible by previous techniques. Some applications of our approach to other groups and other problems in ergodic theory are also briefly discussed.