Uniqueness and ergodic properties of attractive g-measures

Abstract

AbstractWe consider g-measures for the shift on where S is a finite set. For a certain class of continuous g, two g-measures are identified; they are equal if and only if there is a unique g-measure. We prove that the natural extensions of these measures are Bernoulli. With a further restriction on g when S is a two-point set, we show that there is a unique g-measure. We also consider extensions of these results to the non-continuous case.