2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115368A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous $g$-function.Published at http://dx.doi.org/10.1214/074921706000000329 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Dynamical Systems37B10 (Primary)text