Displaying similar documents to “A note on mixing properties of invertible extensions.”

Infinite ergodic index ℤ d -actions in infinite measure

E. Muehlegger, A. Raich, C. Silva, M. Touloumtzis, B. Narasimhan, W. Zhao (1999)

Colloquium Mathematicae

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We construct infinite measure preserving and nonsingular rank one ℤ d -actions. The first example is ergodic infinite measure preserving but with nonergodic, infinite conservative index, basis transformations; in this case we exhibit sets of increasing finite and infinite measure which are properly exhaustive and weakly wandering. The next examples are staircase rank one infinite measure preserving ℤ d -actions; for these we show that the individual basis transformations have conservative...

On weakly mixing and doubly ergodic nonsingular actions

Sarah Iams, Brian Katz, Cesar E. Silva, Brian Street, Kirsten Wickelgren (2005)

Colloquium Mathematicae

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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...

On group extensions of 2-fold simple ergodic actions

Artur Siemaszko (1994)

Studia Mathematica

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Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.