This will be a continuation of the talk by M. I. Cortez, but largely independent of it. I will focus on the example of a non-primitive, non-minimal substition in the plane which generates the "infinite Sierprinski carpet" tiling and show how to find invariant measures for this system. I will then describe the statement in the general case. Under some natural assumptions, the answer can be formulated in terms of the substitution matrix. This is joint work with Maria Isabel Cortez.