Geodesic
Approximate invariance for ergodic actions of amenable groups
Discrete analysis (2019)

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arXiv
We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these techniques, we prove a dynamical generalization of Kneser's celebrated density theorem for subsets in $(\bZ,+)$, valid for any countable amenable group, and we show how it can be used to establish a plethora of new inverse product set theorems for upper and lower asymptotic densities. We provide several examples demonstrating that our results are optimal for the settings under study.
Publié le : 
Michael Björklund; Alexander Fish. Approximate invariance for ergodic actions of amenable groups. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a14/
@article{DAS_2019_a14,
     author = {Michael Bj\"orklund and Alexander Fish},
     title = {Approximate invariance for ergodic actions of amenable groups},
     journal = {Discrete analysis},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2019_a14/}
}
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AU  - Michael Björklund
AU  - Alexander Fish
TI  - Approximate invariance for ergodic actions of amenable groups
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a14/
LA  - en
ID  - DAS_2019_a14
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%T Approximate invariance for ergodic actions of amenable groups
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