Ergodic Theory and Dynamical Systems

Research Article

Countable sections for locally compact group actions

Alexander S. Kechrisa1

a1 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.

(Received March 01 1991)

Footnotes

† Research partially supported by a NSF Grant DMS-9020153.