منابع مشابه
Amenable Actions of Nonamenable Groups
Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known as amenability. Amenable objects like groups, semigroups, algebras, graphs, metric spaces, operator algebras etc. play an important role in different areas of mathematics. A big progress in understanding of th...
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This is a preliminary note containing the proof that every countable non-amenable group admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard Borel space with probability measure. 1. Summary and Notation Let Γ1 y α1 (X1, μ1),Γ2 y α2 (X2, μ2) be Borel measure preserving actions. α1 and α2 are orbit equivalent if there exist conull subsets A1 ⊂ X1, A2 ⊂ ...
متن کاملFølner Tilings for Actions of Amenable Groups
We show that every probability-measure-preserving action of a countable amenable group G can be tiled, modulo a null set, using finitely many finite subsets of G (“shapes”) with prescribed approximate invariance so that the collection of tiling centers for each shape is Borel. This is a dynamical version of the Downarowicz–Huczek– Zhang tiling theorem for countable amenable groups and strengthe...
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It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...
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We generalize two theorems about K-automorphisms from Z to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1994-1250814-5