Geodesic
Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories
Paulina Frej1
1 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 126 (2012) no. 2, pp. 205-216 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We define the space of trajectories of a doubly stochastic operator on $L^1(X,\mu)$ as a shift space $(X^\mathbb N,\nu,\sigma)$, where $\nu$ is a probability measure defined as in the Ionescu–Tulcea theorem and $\sigma$ is the shift transformation. We study connections between the entropy of a doubly stochastic operator and the entropy of the shift on the space of trajectories of this operator.
DOI : 10.4064/cm126-2-5
Keywords: define space trajectories doubly stochastic operator shift space mathbb sigma where probability measure defined ionescu tulcea theorem sigma shift transformation study connections between entropy doubly stochastic operator entropy shift space trajectories operator

Paulina Frej 1

1 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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Paulina Frej. Entropy of a doubly stochastic Markov operator and of 
its shift on the space of trajectories. Colloquium Mathematicum, Tome 126 (2012) no. 2, pp. 205-216. doi: 10.4064/cm126-2-5

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