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Absolutely continuous, invariant measures for dissipative, ergodic transformations

100%
Aaronson J., Meyerovitch T.
Colloquium Mathematicum
|
2008
|
tom 110
|
nr 1
193-199
EN
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.
2
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Predictability, entropy and information of infinite transformations

100%
Aaronson J., Park K.
Fundamenta Mathematicae
|
2009
|
tom 206
|
nr 1
1-21
EN
We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2.
3
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Remarks on the tightness of cocycles

100%
Aaronson J., Weiss B.
Colloquium Mathematicum
|
2000
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tom 84/85
|
nr 2
363-376
EN
We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.
4
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A cut salad of cocycles

81%
Aaronson J., Lemańczyk M., Volný D.
Fundamenta Mathematicae
|
1998
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tom 157
|
nr 2-3
99-119
EN
We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed.
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