# The Mean Ratio Set for <i>ax</i> + <i>b</i> Valued Cocycles

### Karma Dajani

Universiteit Utrecht, Netherlands### Anthony H. Dooley

University of Technology Sydney, Ultimo, Australia

## Abstract

Let *X*=Π∞_t_=1_Zl_(*i*) be acted upon by the group Γ=⊕∞_i_=1_Zl_(*i*) of changes in finitely many coordinates and μ a *G*-measure on *X* which is nonsingular for the Γ-action on *X*. We consider cocycles on (*X, Γ, μ) taking values in the ax + b group. We give a structure theorem for such cocycles, we define 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.*

## Cite this article

Karma Dajani, Anthony H. Dooley, The Mean Ratio Set for <i>ax</i> + <i>b</i> Valued Cocycles. Publ. Res. Inst. Math. Sci. 32 (1996), no. 4, pp. 671–688

DOI 10.2977/PRIMS/1195162716