Continuous bounded cocycles
Résumé
Let $G$ be a minimal second countable locally compact groupoid with Hausdorff unit space and let $E$ be a continuous $G$-Hilbert bundle. We show that a conditionally bounded continuous cocycle $c:G\to r^*E$ is necessarily a continuous coboundary. This is a groupoid version of a classical theorem of Gottschalk and Hedlund.