The mean ratio set for ax+b valued cocycles

Abstract

Let X = Q 1 i=1 Z `(i) be acted upon by the group Q i=1 `(i) i=1 `(i) of changes in nitely many coordinates and a G-measure on X which is nonsingular for the ax+b group. We give a structure theorem for such cocycles, we dene the mean ratio set which is a closed subgroup of the ax + b group and we exhibit for each closed subgroup a cocycle whose mean ratio set is the given subgroup.