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We consider universes that are close to Friedmann-Robertson-Walker in thesense that metric perturbations, their time derivatives and first spatialderivatives are small, but second spatial derivatives are not constrained. Weshow that if we in addition assume that the observer four-velocity is close toits background value and close to the four-velocity which defines thehypersurface of averaging, the redshift and the average expansion rate remainclose to the FRW case. However, this is not true for the angular diameterdistance. The four-velocity assumption implies certain conditions on secondderivatives of the metric and/or the matter content.

Light propagation and the average expansion rate in near-FRW universes