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Amenable equivalence relations and the construction of ergodic averages for group actions. (English) Zbl 1358.37015
Summary: We present a general new method for constructing pointwise ergodic sequences on countable groups which is applicable to amenable as well as to nonamenable groups and treats both cases on an equal footing. The principle underlying the method is that both cases can be viewed as instances of the general ergodic theory of amenable equivalence relations.

MSC:
37A25 Ergodicity, mixing, rates of mixing
37A30 Ergodic theorems, spectral theory, Markov operators
28D15 General groups of measure-preserving transformations
22D40 Ergodic theory on groups
22F10 Measurable group actions
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