A Local Ergodic Theorem.
U. KRENGEL (1968/69)
Inventiones mathematicae
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Displaying similar documents to “Strict measure rigidity for unipotent subgroups of solvable groups.”
A Local Ergodic Theorem.
The ergodic theory of shrinking targets.
Richard Hill, Sanju L. Velani (1995)
Inventiones mathematicae
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An algebraic group associated to an ergodic diffeomorphism
Robert J. Zimmer (1981)
Compositio Mathematica
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Characterizing mildly mixing actions by orbit equivalence of products.
Hawkins, Jane, Silva Cesar, E. (1998)
The New York Journal of Mathematics [electronic only]
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Absolutely continuous, invariant measures for dissipative, ergodic transformations
Jon Aaronson, Tom Meyerovitch (2008)
Colloquium Mathematicae
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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.
Induced and amenable ergodic actions of Lie groups
Robert J. Zimmer (1978)
Annales scientifiques de l'École Normale Supérieure
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Ergodic Theorems for Noncommutative Dynamical Systems.
J.P. Conze, N. Dang-Ngoc (1978)
Inventiones mathematicae
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Infinite ergodic index -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 -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 -actions; for these we show that the individual basis transformations have conservative...
On measure theoretical analogues of the Takesaki structure theorem for type III factors
Alexandre Danilenko, Toshihiro Hamachi (2000)
Colloquium Mathematicae
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The orbit equivalence of type ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type cocycles with values in Abelian groups.
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...