Abstract

We are going to consider a meromorphic function g: $\Re \to \Re,$ which has a constant sign in the upper half plan. We will show that it has a special form$${\rm g(z) = A} + \varepsilon\left\lbrack Bz- \sum\sb{s} p\sb{s} ({1\over{z-c\sb{s}}}{+}{1\over {c\sb{s}}})\right\rbrack$$where the poles are real and simples. Subsequently, we will demonstrate that it has an absolutely continuous invariant measure. Finally, we will present an example to emphasise the use of this transformation.