“…They constitute an important class of stochastic models, which includes, for example, Markov chains, stochastic models that exhibit nonuniqueness and models that are not Gibbsian (Fernández et al, 2011). The question of uniqueness of g-measures was extensively studied and important progresses have been obtained in several areas related to probability and ergodic theory, from the seminal works of Onicescu & Mihoc (1935); Doeblin & Fortet (1937) to recent advances in Johansson et al (2012); Gallo & Paccaut (2013), and the contributions of Harris (1955); Keane (1972); Walters (1975); Lalley (1986); Stenflo (2003); Fernández & Maillard (2005) among many others. Notwithstanding, the problem of non-uniqueness is much less understood and the literature is still based on few examples (Bramson & Kalikow, 1993;Hulse, 2006;Berger et al, 2005).…”