Results 221 to 230 of about 33,406 (259)

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
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In General a Measure Preserving Transformation is Mixing

The Annals of Mathematics, 1944
Not ...
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𝑘-parameter semigroups of measure-preserving transformations

Transactions of the American Mathematical Society, 1973
An individual ergodic theorem is proved for semigroups of measure-preserving transformations depending on k real parameters, which generalizes N. Wiener’s ergodic theorem.
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Isomorphism of measure preserving transformations

Kybernetika, 1987
The \(\delta\)-entropy of endomorphism has been defined. This entropy reduces to the Shannon entropy of endomorphism for \(\delta =1\). The two isomorphic measure preserving transformations have the same \(\delta\)- entropy of endomorphism.
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The ergodic infinite measure preserving transformation of boole

Israel Journal of Mathematics, 1973
G. Boole proved that the transformation φ of the real line, defined by φ(x)=x−1/x, preserves Lebesgue measure. A general method is applied to proving that φ is ergodic. Some further applications of the method are also indicated.
Adler, Roy. L., Weiss, Benjamin
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Characterizations of Measurability-Preserving Ergodic Transformations

Sarajevo Journal of Mathematics
Let ($S, \mathfrak{A}, \mu$) be a finite measure space and let $\phi: S \rightarrow S$ be a transformation which preserves the measure $\mu$. The purpose of this paper is to give some (measure theoretical) necessary and sufficient conditions for the transformation $\phi$ to be measurability-preserving ergodic with respect to $\mu$. The obtained results
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LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS

Russian Mathematical Surveys, 1967
CONTENTSIntroduction § 1. Preliminaries from measure theory § 2. Isometric operators § 3. Measure-preserving transformations § 4. Entropy of a measurable partition § 5. Mean conditional entropy § 6. Spaces of partitions § 7. Fundamental lemmas § 8. Properties of the function h(T, ξ) § 9. Entropy of an endomorphism § 10.
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Measure preserving transformations similar to Markov shifts

Israel Journal of Mathematics, 2009
A \(c\)-factor map between infinite measure-preserving systems \((X,\mathcal B,\mu,T)\) and \((X',\mathcal B',\mu',T')\) is a measurable map \(p:(X,\mathcal B)\to(X',\mathcal B')\) with \(p\circ T=T'\circ p\) and \(\mu\circ p^{-1}=c\mu'\). Infinite measure-preserving systems are said to be similar if they share an extension: that is, there are ...
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Spectral Properties for Invertible Measure Preserving Transformations

Canadian Journal of Mathematics, 1973
An invertible measure preserving transformation T on the unit interval I generates a unitary operator U on the space L2(I) of Lebesque square integrable functions given by (Uf)(x) = f(Tx) for all f in L2(I) and x in I. By definitionfor all f , g in L2(I), the bar denoting complex conjugation.
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A New Clustering Preserving Transformation for k-Means Algorithm Output

Lecture Notes in Computer Science, 2022
Mieczysław Kłopotek, Kłopotek Mieczysław A   +1 more
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