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Criteria for $\bar {d}$-continuity

1998; American Mathematical Society; Volume: 350; Issue: 8 Linguagem: Inglês

10.1090/s0002-9947-98-01923-0

1088-6850

Zaqueu Coelho, Anthony Quas,

Advanced Topology and Set Theory

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.