Geodesic
On weakly mixing and doubly ergodic nonsingular actions
Sarah Iams 1   ; Brian Katz 2   ; Cesar E. Silva 3   ; Brian Street 4   ; Kirsten Wickelgren 5
1 Williams College Williamstown, MA 01267, U.S.A. and Emmanuel College Cambridge, CB2 3AP, UK
2 Williams College Williamstown, MA 01267, U.S.A. and Department of Mathematics University of Texas Austin, TX 78712, U.S.A.
3 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.
4 University of Virginia Charlottesville, VA 22903, U.S.A. and Department of Mathematics Princeton University Princeton, NJ 08544, U.S.A.
5 Harvard University Cambridge, MA 02138, U.S.A. and Department of Mathematics Stanford University Palo Alto, CA 94305, U.S.A.
Colloquium Mathematicum, Tome 103 (2005) no. 2, pp. 247-264 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm103-2-10
Keywords: study weak mixing double ergodicity nonsingular actions locally compact polish abelian groups nonsingular action weakly mixing only cocompact subgroups action restricted weakly mixing doubly ergodic nonsingular action weakly mixing construct infinite measure preserving flow weakly mixing doubly ergodic construct infinite measure preserving flow whose cartesian square ergodic

Sarah Iams  1   ; Brian Katz  2   ; Cesar E. Silva  3   ; Brian Street  4   ; Kirsten Wickelgren  5

1 Williams College Williamstown, MA 01267, U.S.A. and Emmanuel College Cambridge, CB2 3AP, UK
2 Williams College Williamstown, MA 01267, U.S.A. and Department of Mathematics University of Texas Austin, TX 78712, U.S.A.
3 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.
4 University of Virginia Charlottesville, VA 22903, U.S.A. and Department of Mathematics Princeton University Princeton, NJ 08544, U.S.A.
5 Harvard University Cambridge, MA 02138, U.S.A. and Department of Mathematics Stanford University Palo Alto, CA 94305, U.S.A. 
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     title = {On weakly mixing and doubly ergodic  nonsingular actions},
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Sarah Iams; Brian Katz; Cesar E. Silva; Brian Street; Kirsten Wickelgren. On weakly mixing and doubly ergodic  nonsingular actions. Colloquium Mathematicum, Tome 103 (2005) no. 2, pp. 247-264. doi: 10.4064/cm103-2-10

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