Square summability of variations of \(g\)-functions and uniqueness of \(g\)-measures (Q1429365)

The paper is concerned with the uniqueness problem for \(g\)-measures introduced by \textit{M. Keane} [Invent. Math. 16, 309--324 (1972; Zbl 0241.28014)]. The authors prove the uniqueness of \(g\)-measures for the case when the corresponding \(g\)-functions satisfy the summability of variations condition. Conditions of the uniqueness of general \(g\)-measures (i.e., the case with general potentials) are considered as well. The main application of these results is the analysis of ergodic properties of a class of iterated function systems, where \(g\)-functions correspond to probabilistic weights.