On non-regular g-measures

TL;DR

This paper investigates conditions under which non-regular g-measures exist and are unique, focusing on the role of discontinuity points and topological pressure in their characterization.

Contribution

It establishes existence of stationary g-measures under weaker assumptions than non-nullness and provides criteria for their uniqueness based on continuity properties.

Findings

Existence of stationary g-measures with discontinuity points of negative topological pressure.

Conditions for uniqueness of g-measures based on continuity set properties.

Abstract

We prove that g-functions whose set of discontinuity points has strictly negative topological pressure and which satisfy an assumption that is weaker than non-nullness, have at least one stationary g-measure. We also obtain uniqueness by adding conditions on the set of continuity points.