Criteria for 𝑑̄-continuity

Coelho, Zaqueu; Quas, Anthony

doi:10.1090/S0002-9947-98-01923-0

Criteria for $\bar {d}$-continuity
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by Zaqueu Coelho and Anthony N. Quas

Trans. Amer. Math. Soc. 350 (1998), 3257-3268

DOI: https://doi.org/10.1090/S0002-9947-98-01923-0

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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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