Pointwise theorems for amenable groups
Copyright policy )Pointwise theorems for amenable groups
In this paper we describe proofs of the pointwise ergodic theorem and Shannon-McMillan-Breiman theorem for discrete amenable groups, along Følner sequences that obey some restrictions. These restrictions are mild enough so that such sequences exist for all amenable groups.
Shannon-MacMillan-Breiman theorem, Ergodic theorems, spectral theory, Markov operators, Strong limit theorems, General groups of measure-preserving transformations and dynamical systems, Means on groups, semigroups, etc.; amenable groups, pointwise ergodic theorem, discrete amenable groups, Relations of ergodic theory with number theory and harmonic analysis, General groups of measure-preserving transformations, Følner sequences
Shannon-MacMillan-Breiman theorem, Ergodic theorems, spectral theory, Markov operators, Strong limit theorems, General groups of measure-preserving transformations and dynamical systems, Means on groups, semigroups, etc.; amenable groups, pointwise ergodic theorem, discrete amenable groups, Relations of ergodic theory with number theory and harmonic analysis, General groups of measure-preserving transformations, Følner sequences
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