Quasinormal subrelations of ergodic equivalence relations
Author:
Alexandre I. Danilenko
Journal:
Proc. Amer. Math. Soc. 126 (1998), 33613370
MSC (1991):
Primary 28D99, 46L55
MathSciNet review:
1610944
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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 FeldmanSutherlandZimmer.) 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:
http://dx.doi.org/10.1090/S0002993998049090
PII:
S 00029939(98)049090
Received by editor(s):
April 10, 1997
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1998
American Mathematical Society
