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On weakly mixing and doubly ergodic nonsingular actions

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Iams S., Katz B., Silva C., Street B., Wickelgren K.

Colloquium Mathematicum

2005

tom 103

nr 2

247-264

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Iams S.

1 Katz B.

1 Silva C.

1 Street B.

1 Wickelgren K.

1 2005

Wyniki wyszukiwania

On weakly mixing and doubly ergodic nonsingular actions