## Criteria for $\bar {d}$-continuity

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- by Zaqueu Coelho and Anthony N. Quas PDF
- Trans. Amer. Math. Soc.
**350**(1998), 3257-3268 Request permission

## 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.## References

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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
- Email: zcoelho@fc.up.pt
**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
- MR Author ID: 317685
- Email: quasa@msci.memphis.edu
- Received by editor(s): March 7, 1996
- Received by editor(s) in revised form: September 18, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 3257-3268 - MSC (1991): Primary 28D05, 60G10
- DOI: https://doi.org/10.1090/S0002-9947-98-01923-0
- MathSciNet review: 1422894