On Non-Negative Measurable Solutions of a Difference Functional Equation

Following M. Laczkovich [5] we consider the iterative functional equationand its non-negative measurable solutions . In the mentioned paper the author studies non-negative Lebesgue measurable solutions defined on the real line. It is our goal to consider this problem both in more dimensions and from a more abstract point of view, in particular to get also topological version of his result.