Quasi-Invariant Measures for Some Amenable Groups Acting on the Line

We show that if G is a solvable group acting on the line and if there is T ∈ G having no fixed points, then there is a Radon measure μ on the line quasi-invariant under G. In fact, our method allows for the same conclusion for G inside a class of groups that is closed under extensions and contains all solvable groups and all groups of subexponential growth. © 2018, Mathematical Sciences Publishers. All rights reserved.