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Countable sections for locally compact group actions

  • Alexander S. Kechris (a1)

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.

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[A] W. Ambrose . Representation of ergodic flows. Ann. of Math. 42 (1941), 723739.

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[HKL] L. Harrington , A. S. Kechris & A. Louveau . A Glimm—Effros dichotomy for Borel equivalence relations. J. Amer. Math. Soc. 3 (1990), 903928.

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[Var] V. S. Varadarajan . Groups of automorphisms of Borel spaces. Trans. Amer. Math. Soc. 109 (1963), 191220.

[W] V. M. Wagh . A descriptive version of Ambrose's representation theorem for flows. Proc. Ind. Acad. Sci. (Math. Sci.) 98 (1988), 101108.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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