Tail fields generated by symbol counts in measure-preserving systems
Volume 101 / 2004
Colloquium Mathematicum 101 (2004), 9-23
MSC: 37A05, 37A35, 37A50.
DOI: 10.4064/cm101-1-2
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 $(\alpha,T)$ which has a direct Bernoulli factor there is a generating partition $\beta$ whose one-sided super-tail equals the usual one-sided tail of $\beta$. 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.)
