Finitarily Bernoulli factors are dense

Stephen Shea. "Finitarily Bernoulli factors are dense." Fundamenta Mathematicae 223.1 (2013): 49-54. <http://eudml.org/doc/283344>.

@article{StephenShea2013,
abstract = {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'.},
author = {Stephen Shea},
journal = {Fundamenta Mathematicae},
keywords = {Bernoulli scheme; d-bar metric; finitary isomorphism; r-process},
language = {eng},
number = {1},
pages = {49-54},
title = {Finitarily Bernoulli factors are dense},
url = {http://eudml.org/doc/283344},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Stephen Shea
TI - Finitarily Bernoulli factors are dense
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 1
SP - 49
EP - 54
AB - 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'.
LA - eng
KW - Bernoulli scheme; d-bar metric; finitary isomorphism; r-process
UR - http://eudml.org/doc/283344
ER -