Quasinormal subrelations of ergodic

equivalence relations

Author:
Alexandre I. Danilenko

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3361-3370

MSC (1991):
Primary 28D99, 46L55

DOI:
https://doi.org/10.1090/S0002-9939-98-04909-0

MathSciNet review:
1610944

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a notion of quasinormality for a nested pair of ergodic discrete hyperfinite equivalence relations of type . (This is a natural extension of the normality concept due to Feldman-Sutherland-Zimmer.) Such pairs are characterized by an irreducible pair of countable amenable groups or rather (some special) their Polish closure . We show that ``most'' of the ergodic subrelations of are quasinormal and classify them. An example of a nonquasinormal subrelation is given. We prove as an auxiliary statement that two cocycles of with dense ranges in a Polish group are weakly equivalent.

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Additional Information

**Alexandre I. Danilenko**

Affiliation:
Department of Mechanics and Mathematics, Kharkov State University, Freedom square 4, Kharkov, 310077, Ukraine

Email:
danilenko@ilt.kharkov.ua

DOI:
https://doi.org/10.1090/S0002-9939-98-04909-0

Received by editor(s):
April 10, 1997

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society