Nonamenability and Borel paradoxical decompositions for locally compact groups
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- by Alan L. T. Paterson PDF
- Proc. Amer. Math. Soc. 96 (1986), 89-90 Request permission
Abstract:
We show that a locally compact group $G$ is not amenable if and only if it admits a Borel paradoxical decomposition.References
- William R. Emerson, The Hausdorff paradox for general group actions, J. Functional Analysis 32 (1979), no. 2, 213–227. MR 534675, DOI 10.1016/0022-1236(79)90055-7
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549 D. König, Sur les correspondences multivoques des ensembles, Fund. Math. 8 (1926), 114-134.
- George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423
- Neil W. Rickert, Some properties of locally compact groups, J. Austral. Math. Soc. 7 (1967), 433–454. MR 0219656
- Neil W. Rickert, Amenable groups and groups with the fixed point property, Trans. Amer. Math. Soc. 127 (1967), 221–232. MR 222208, DOI 10.1090/S0002-9947-1967-0222208-6 A. Tarski, Algebraische Fassung des Massproblems, Fund. Math. 31 (1938), 47-66.
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 89-90
- MSC: Primary 43A07; Secondary 22D05
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813817-9
- MathSciNet review: 813817