On finitary shifts (Q1389877)

Studying functionals of Markov chains, \textit{A. Heller} [Ann. Math. Stat. 36, 1286-1291 (1965; Zbl 0139.34603)] introduced a class of processes called \({\mathcal F}\)-processes. The main purpose of the paper is to give a probabilistic description of \({\mathcal F}\)-processes, and to show that the class of \({\mathcal F}\)-processes is closed under factors, products and roots. It is shown that the class of \({\mathcal F}\)-shifts is not closed under taking inverse limits.