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

Des points fixes communs pour des diff\'eomorphismes de S^2 qui commutent et pr\'eservent une mesure de probabilit\'e