Finitarily Bernoulli factors are dense

• Autorzy: Stephen Shea
• Języki publikacji: EN

Abstrakty

EN

It is not known if every finitary factor of a Bernoulli scheme is finitarily isomorphic to a Bernoulli scheme (is finitarily Bernoulli). In this paper, for any Bernoulli scheme X, we define a metric on the finitary factor maps from X. We show that for any finitary map f: X → Y, there exists a sequence of finitary maps fₙ: X → Y(n) that converges to f, where each Y(n) is finitarily Bernoulli. Thus, the maps to finitarily Bernoulli factors are dense. Let (X(n)) be a sequence of Bernoulli schemes such that each Y(n) is finitarily isomorphic to X(n). Let X' be a Bernoulli scheme with the same entropy as Y. Then we also show that (X(n)) can be chosen so that there exists a sequence of finitary maps to the X(n) that converges to a finitary map to X'.

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 60G10: Stationary processes
• 28D20: Entropy and other invariants
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 1
• Strony: 49-54

Daty

wydano

2013

Twórcy

autor

Stephen Shea

• Department of Mathematics, St. Anselm College, 100 St. Anselm Drive #1792, Manchester, NH 03102, U.S.A.

Identyfikatory

DOI

10.4064/fm223-1-3