Topic
Hyperfinite set
About: Hyperfinite set is a research topic. Over the lifetime, 68 publications have been published within this topic receiving 1175 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, a C*-algebra whose set of pure states is not closed is studied. But it is not the first example of a C * -algebra with a set of states that is not necessarily closed, cf.
Abstract: algebras. The w*-closure of the pure states of one of these algebras is the set of all states of the algebra. This is not the first example of a C*-algebra whose set of pure states is not closed, cf. [7]. In ?3 we classify the irreducible representations of uniformly hyperfinite algebras according to unitary equivalence. In ??4 and 5 we study certain representations of uniformly hyperfinite algebras.
415 citations
TL;DR: In this article, the authors classified hyperfinite type IIIλsubfactors of the same index of the Powers factor for 0 <λ < 1, such that the principal graph of the corresponding type II1inclusion is of one of the following: an,n⩾2,E6,E8, or a finite group.
54 citations
TL;DR: In this paper, it was shown that any hyperfinite factor of type III 0 is the cross product of an abelian von Neumann algebra by a single automorphism.
42 citations
TL;DR: In this paper, the authors define a class of equivalence relations with polynomial growth and show that such relations always support finite invariant measures and are hyperfinite, i.e., they always support a family of finite invariants on transversals.
Abstract: We define a class of equivalence relations with polynomial growth and show that such relations always support finite invariant measures and are hyperfinite. In particular, foliations of polynomial growth define hyperfinite equivalence relations with respect to any family of finite invariant measures on transversals. We also extend a result of Dye for countable groups to show that if a locally compact second countable groupG acts freely on a Lebesgue spaceX with finite invariant measure, so that the orbit relation onX is hyperfinite, thenG is amenable.
20 citations
1 Feb 1976
TL;DR: In this article, a countable abelian group G acts nonsingularly and aperiodically on Lebesgue space (X, u) for each finite subset A c G and e > 0 3 finite B c G with {bF: b E B) disjoint and u[(FnaEAB a)F] > 1 e.
Abstract: HEOREM 1. Let the countable abelian group G act nonsingularly and aperiodically on Lebesgue space (X, u). Then for each finite subset A c G and e > 0 3 finite B c G and F c X with {bF: b E B) disjoint and u[(FnaEAB a)F] > 1 e. THEOREM 2. Every nonsingular action of a countable abelian group on a Lebesgue space is hyperfinite.
19 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 1 |
| 2016 | 3 |
| 2015 | 6 |
| 2013 | 3 |
| 2011 | 1 |
| 2010 | 1 |