Transactions of the American Mathematical Society

Author(s): Zaqueu Coelho; Anthony N. Quas
Journal: Trans. Amer. Math. Soc. 350 (1998), 3257-3268.
MSC (1991): Primary 28D05, 60G10
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Abstract: Bernoullicity is the strongest mixing property that a measure-theoretic dynamical system can have. This is known to be intimately connected to the so-called $\bar d$ metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend $\bar d$ -continuously on the parameters. At points where there is $\bar d$ -continuity, it is often straightforward to establish that the measures have the Bernoulli property.

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Zaqueu Coelho
Affiliation: Instituto de Matemática e Estatítica, Universidade de São Paulo, São Paulo, Brazil
Address at time of publication: Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, Rua das Taipas 135, P-4050 Porto, Portugal
Email: zcoelho@fc.up.pt

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