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Countable sections for locally compact group actions

Published online by Cambridge University Press:  19 September 2008

Alexander S. Kechris
Affiliation:
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

It has been shown by J. Feldman, P. Hahn and C. C. Moore that every non-singular action of a second countable locally compact group has a countable (in fact so-called lacunary) complete measurable section. This is extended here to the purely Borel theoretic category, consisting of a Borel action of such a group on an analytic Borel space (without any measure). Characterizations of when an arbitrary Borel equivalence relation admits a countable complete Borel section are also established.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1992

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