Quasi-invariant measures for a foliation and limits of leafwise averages

In this Note, we generalize a result of Goodman-Plante, who characterizes limit points of averaging sequences as holonomy invariant transverse measures. We prove an analogous result for some leafwise averages, weighted with a cocycle Delta, whose limit points are a product of a quasi-invariant transverse measure with respect to A with a leafwise measure.