Tail fields generated by symbol counts in measure-preserving systems

Karl Petersen, and Jean-Paul Thouvenot. "Tail fields generated by symbol counts in measure-preserving systems." Colloquium Mathematicae 101.1 (2004): 9-23. <http://eudml.org/doc/286588>.

@article{KarlPetersen2004,
abstract = {A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator. (This partially answers a question of Petersen and Schmidt.)},
author = {Karl Petersen, Jean-Paul Thouvenot},
journal = {Colloquium Mathematicae},
keywords = {tail field; -system; super- system; Bernoulli system; exchangeable algebra; entropy},
language = {eng},
number = {1},
pages = {9-23},
title = {Tail fields generated by symbol counts in measure-preserving systems},
url = {http://eudml.org/doc/286588},
volume = {101},
year = {2004},
}

TY - JOUR
AU - Karl Petersen
AU - Jean-Paul Thouvenot
TI - Tail fields generated by symbol counts in measure-preserving systems
JO - Colloquium Mathematicae
PY - 2004
VL - 101
IS - 1
SP - 9
EP - 23
AB - A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator. (This partially answers a question of Petersen and Schmidt.)
LA - eng
KW - tail field; -system; super- system; Bernoulli system; exchangeable algebra; entropy
UR - http://eudml.org/doc/286588
ER -