Countable sections for locally compact group actions

DOI10.1017/S0143385700006751zbMath0761.28014MaRDI QIDQ4024956

Alexander S. Kechris

Publication date: 18 February 1993

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

locally compact groupcountable measurable sectionBorel actionnon-singular actioncountable complete Borel section

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15)

Related Items (38)

The classification problem for torsion-free abelian groups of finite rank ⋮ Reduction of cocycles with hyperbolic targets ⋮ Non-classification of Cartan subalgebras for a class of von Neumann algebras ⋮ COUNTABLE BOREL EQUIVALENCE RELATIONS ⋮ Borel equivalence relations and cardinal algebras ⋮ Borel globalizations of partial actions of Polish groups ⋮ Abelian group actions and hypersmooth equivalence relations ⋮ Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension ⋮ Lebesgue orbit equivalence of multidimensional Borel flows: A picturebook of tilings ⋮ The classification problem for operator algebraic varieties and their multiplier algebras ⋮ CONTINUOUS LOGIC AND BOREL EQUIVALENCE RELATIONS ⋮ $\sigma $-lacunary actions of Polish groups ⋮ Stationary measures and closed invariants on homogeneous spaces ⋮ Projections of Patterson-Sullivan measures and the dichotomy of Mohammadi-Oh ⋮ Selection theorems and treeability ⋮ The classification of hypersmooth Borel equivalence relations ⋮ Non-treeability for product group actions ⋮ Countable Sections for Locally Compact Group Actions. II ⋮ The Structure of Hyperfinite Borel Equivalence Relations ⋮ Regular cross sections of Borel flows ⋮ On the complexity of the isomorphism relation for fields of finite transcendence degree ⋮ Amenable Actions of Groups ⋮ Borel equivalence relations and classifications of countable models ⋮ Borel actions of Polish groups ⋮ On Polish groups admitting non-essentially countable actions ⋮ On the complexity of the classification problem for torsion-free abelian groups of rank two. ⋮ Minimal model-universal flows for locally compact Polish groups ⋮ On time change equivalence of Borel flows ⋮ Rigidity properties of Borel ideals on the integers ⋮ RECURRENCE AND THE EXISTENCE OF INVARIANT MEASURES ⋮ Analytic ideals and their applications ⋮ On the complexity of the isomorphism relation for finitely generated groups ⋮ Linear algebraic groups and countable Borel equivalence relations ⋮ Splitting of nonnegatively curved leaves in minimal sets of foliations ⋮ The space of composants of an indecomposable continuum ⋮ Superrigidity and countable Borel equivalence relations ⋮ Polish groupoids and functorial complexity ⋮ On the classification of automorphisms of trees

Cites Work

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• Topologies on measured groupoids
• Countable sections for free actions of groups
• A selection theorem for group actions
• Representation of ergodic flows
• Borel Structure in Groups and Their Duals
• A Glimm-Effros Dichotomy for Borel Equivalence Relations
• On the Measurability of Orbits in Borel Actions
• Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
• Measure and category in effective descriptive set theory
• Groups of Automorphisms of Borel Spaces

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