Results 221 to 230 of about 364,452 (273)

Commuting measure-preserving transformations

Israel Journal of Mathematics, 1972
Let φ1, ... ,φd be commuting measure-preserving transformations, \( \phi ^l \equiv \phi _1^{l_1 } \phi _2^{l_2 } \cdot \cdot \cdot \phi _d^{l_d } ,\Phi = \left\{ {\phi ^l } \right\} \). The Kakutani-Rokhlin tower theorem is proved in a refined form for non-periodic groups Φ, and the Shannon-McMillan theorem is extended to ergodic groups.
Katznelson, Yitzhak, Weiss, Benjamin
openaire   +2 more sources

Jointly ergodic measure-preserving transformations

Israel Journal of Mathematics, 1984
The notion of ergodicity of a measure preserving transformation is generalized to finite sets of transformations. The main result is that, if \(T_ 1,T_ 2,...,T_ s\) are invertible commuting measure preserving transformations, of a probability space (X,\({\mathcal B},\mu)\), then \[ \frac{1}{N-M}\sum^{N-1}_{n=M}T^ n_ 1f_ 1\cdot T^ n_ 2f_ 2\cdot...\cdot ...
Berend, Daniel, Bergelson, Vitaly
openaire   +2 more sources

Measurability – Preserving Weakly Mixing Transformations

Sarajevo Journal of Mathematics
In this paper we investigate measure-theoretic properties of the class of all weakly mixing transformations on a finite measure space which preserve measurability. The main result in this paper is the following theorem: If $\phi $ is a weakly mixing transformation on a finite measure space $( S, \mathcal A , \mu )$ with the property that $\phi ...
Huse Fatkić
openaire   +2 more sources

Measure-preserving transformations, copulae and compatibility

2008
We study the relationship between copulas and measure-preserving transformations on the Borel sets of the u it interval. This also allows to investigate the connection with a restricted compatibility problem for copulas. To this end, in order to construct a 3-copula from two given 2-copulas A and B, we modify the *-operation introduced by Darsow et al.,
KOLESAROVA, A   +3 more
openaire   +3 more sources

Generic measure preserving transformations and the closed groups they generate

Inventiones Mathematicae, 2021
We show that, for a generic measure preserving transformation T , the closed group generated by T is not isomorphic to the topological group $$L^0(\lambda , {{\mathbb {T}}})$$ L 0 ( λ , T ) of all Lebesgue measurable functions from [0, 1] to $${\mathbb ...
Slawomir Solecki
semanticscholar   +1 more source

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