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.)
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-2,
author = {Karl Petersen and Jean-Paul Thouvenot},
title = {Tail fields generated by symbol counts in measure-preserving systems},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {9-23},
zbl = {1057.37002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-2}
}
Karl Petersen; Jean-Paul Thouvenot. Tail fields generated by symbol counts in measure-preserving systems. Colloquium Mathematicae, Tome 100 (2004) pp. 9-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-2/