Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
- 1 June 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 1 (2) , 223-236
- https://doi.org/10.1017/s014338570000924x
Abstract
This paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G: strong ergodicity (i.e. the non-existence of almost invariant sets), uniqueness of G-invariant means on the measure space carrying the group action, and certain cohomological properties. Using these properties one can characterize all actions of amenable groups and of groups with Kazhdan's property T. For groups which fall in between these two definations these notions lead to some interesting examples.Keywords
This publication has 12 references indexed in Scilit:
- Almost Invariant SetsBulletin of the London Mathematical Society, 1981
- Property T and asymptotically invariant sequencesIsrael Journal of Mathematics, 1980
- Asymptotically invariant sequences and an action of SL (2,Z) on the 2-sphereIsrael Journal of Mathematics, 1980
- Counterexamples in ergodic theory and number theoryMathematische Annalen, 1979
- A class of probability measures on groups arising from some problems in ergodic theoryPublished by Springer Nature ,1979
- Amenable ergodic group actions and an application to Poisson boundaries of random walksJournal of Functional Analysis, 1978
- On the cohomology of a hyperfinite actionMonatshefte für Mathematik, 1977
- Ergodic equivalence relations, cohomology, and von Neumann algebras. ITransactions of the American Mathematical Society, 1977
- Probability Measures on Metric Spaces.Journal of the American Statistical Association, 1968
- PROBABILITY MEASURES IN A METRIC SPACEPublished by Elsevier ,1967