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Quelques propriétés des systèmes dynamiques qui se decomposent en un produit de deux systèmes dont l’un est un schema de Bernoulli. (French) Zbl 0329.28008


MSC:

28D05 Measure-preserving transformations
60G10 Stationary stochastic processes
Full Text: DOI

References:

[1] Berg, K., Convolution of invariant measures. Maximal entropy, Math. Systems Theory, 3, 146-151 (1969) · Zbl 0179.08301 · doi:10.1007/BF01746521
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[3] Katznelson, Y.; Weiss, B., Commuting measure preserving transformations, Israel J. Math., 12, 161-173 (1972) · Zbl 0239.28014
[4] Ornstein, D. S., Imbedding Bernoulli shifts in flows. Contribution to Ergodic Theory and Probability, 178-218 (1970), Berlin: Springer-Verlag, Berlin · Zbl 0227.28013 · doi:10.1007/BFb0060654
[5] Friedman, A. N.; Ornstein, D. S., On isomorphism of weak Bernoulli transformations, Advances in Math., 5, 365-394 (1970) · Zbl 0203.05801 · doi:10.1016/0001-8708(70)90010-1
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[8] Ornstein, D. S., Some new results in the Kolmogorov-Sinai Theory of entropy and ergodic Theory, Bull. Amer. Math. Soc., 77, 878-890 (1971) · Zbl 0269.60032 · doi:10.1090/S0002-9904-1971-12803-3
[9] Ornstein, D. S., An application of ergodic theory to probability theory, Ann. Probability, 1, 43-65 (1973) · Zbl 0282.28009
[10] Ornstein, D. S.; Shields, P. C., An uncountable family of K automorphisms, Advances in Math., 10, 63-88 (1973) · Zbl 0251.28004 · doi:10.1016/0001-8708(73)90098-4
[11] M. Smorodinsky,Ergodic Theory, Entropy, Lecture Notes in Mathematics, 1971, p. 214. · Zbl 0213.07502
[12] M. Smorodinsky,A partition for a Bernoulli shift that is not weak Bernoulli, Math. Systems Theory5 (1971). · Zbl 0226.60066
[13] Thouvenot, J. P., Convergence en moyenne de l’information pour l’action de Z^2, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24, 135-137 (1972) · Zbl 0266.60037 · doi:10.1007/BF00532539
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