Weakly mixing but not mixing quasi-Markovian processes

Kowalski, Zbigniew

Studia Mathematica, Tome 141 (2000), p. 235-244 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (f,α) be the process given by an endomorphism f and by a finite partition $α = {A_{i}}_{i = 1}^{s}$ of a Lebesgue space. Let E(f,α) be the class of densities of absolutely continuous invariant measures for skew products with the base (f,α). We say that (f,α) is quasi-Markovian if $E (f, α) \subset g : ⋁_{{B_{i}}_{i = 1}^{s}} s u p p g = ⋃_{i = 1}^{s} A_{i} \times B_{i}$ . We show that there exists a quasi-Markovian process which is weakly mixing but not mixing. As a by-product we deduce that the set of all coboundaries which are measurable with respect to the ’chequer-wise’ partition for σ × S, where σ is a Bernoulli shift and S is a weakly mixing automorphism, consists of constants.

Publié le : 2000-01-01

Zbl 0977.28008

EUDML-ID : urn:eudml:doc:216800

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     author = {Zbigniew Kowalski},
     title = {Weakly mixing but not mixing quasi-Markovian processes},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {235-244},
     zbl = {0977.28008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p235bwm}
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Kowalski, Zbigniew. Weakly mixing but not mixing quasi-Markovian processes. Studia Mathematica, Tome 141 (2000) pp. 235-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p235bwm/

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