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We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted 'geodesic light-cone' coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called 'redshift drift' in a generic inhomogeneous Universe.
Gasperini et al. (Tue,) studied this question.