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Criteria for $\bar d$-continuity

Authors: Zaqueu Coelho and Anthony N. Quas
Journal: Trans. Amer. Math. Soc. 350 (1998), 3257-3268
MSC (1991): Primary 28D05, 60G10
MathSciNet review: 1422894
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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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Additional Information

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

Anthony N. Quas
Affiliation: Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge, CB2 1SB, England
Address at time of publication: Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152

Keywords: Bernoulli, coupling, $g$-measure
Received by editor(s): March 7, 1996
Received by editor(s) in revised form: September 18, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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