Des points fixes communs pour des diff\'eomorphismes de S² qui commutent et pr\'eservent une mesure de probabilit\'e

We prove the existence of common fixed points for commuting homeomorphisms of the plane R^2 or the sphere S^2, which preserve a probability measure. For example: some commuting C^1-diffeomorphisms of S^2, which are sufficiently close to the identity and preserve a probability measure whose support is not a single point, have at least two common fixed points.