  It is a common assumption amongst astronomers that, in the determination of
the distances of remote sources from their apparent brightness, the cumulative
gravitational lensing due to the matter in all the galaxies is the same, on
average, as if the matter were uniformly distributed throughout the cosmos. The
validity of this assumption is considered here by way of general Newtonian
perturbations of Friedman-Robertson-Walker (FRW) cosmologies. The analysis is
carried out in synchronous gauge, with particular attention to an additional
gauge condition that must be imposed. The mean correction to the apparent
magnitude-redshift relation is obtained for an arbitrary mean density
perturbation. In the case of a zero mean density perturbation, when the
intergalactic matter has a dust equation of state, then there is indeed a
zero-mean first order correction to the apparent magnitude-redshift relation
for all redshifts. Point particle and Swiss cheese models are considered as
particular cases.
