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Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories

Paulina Frej (2012)

Colloquium Mathematicae

We define the space of trajectories of a doubly stochastic operator on L¹(X,μ) as a shift space ( X , ν , σ ) , where ν is a probability measure defined as in the Ionescu-Tulcea theorem and σ 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.

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