On weakly mixing and doubly ergodic nonsingular actions

Published

Journal Article

© 2005, Instytut Matematyczny. All rights reserved. We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving flow whose cartesian square is ergodic.

Full Text

Duke Authors

Cited Authors

  • Iams, S; Katz, B; Silva, CE; Street, B; Wickelgren, K

Published Date

  • January 1, 2005

Published In

Volume / Issue

  • 103 / 2

Start / End Page

  • 247 - 264

Electronic International Standard Serial Number (EISSN)

  • 1730-6302

International Standard Serial Number (ISSN)

  • 0010-1354

Digital Object Identifier (DOI)

  • 10.4064/cm103-2-10

Citation Source

  • Scopus