Skip to main content
×
Home
    • Aa
    • Aa

Countable sections for locally compact group actions

  • Alexander S. Kechris (a1)
Abstract
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.

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

[B] J. Burgess . A selection theorem for group actions. Pac. J. Math. 80 (1979), 333336.

[FM] J. Feldman & C. C. Moore . Ergodic equivalence relations, cohomology and von Neumann algebras, I. Trans. Amer. Math. Soc. 234 (1977), 289324.

[FR] J. Feldman & A. Ramsay . Countable sections for free actions of groups. Adv. Math. 55 (1985), 224227.

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

[Ke1] A. S. Kechris . Measure and category in effective descriptive set theory. Ann. Math. Logic 5 (1973), 337384.

[Ma] G. W. Mackey . Borel structures in groups and their duals. Trans. Amer. Math. Soc. 85 (1957), 134165.

[Mi] D. Miller . On the measurability of orbits in Borel actions. Proc. Amer. Math. Soc. 63 (1977), 165170.

[R1] A. Ramsay . Topologies on measured groupoids. J. Fund. Anal. 47 (1982), 314343.

[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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 108 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 17th October 2017. This data will be updated every 24 hours.