  The observed properties of high redshift galaxies depend on the underlying
foreground distribution of large scale structure, which distorts their
intrinsic properties via gravitational lensing. We focus on the regime where
the dominant contribution originates from a single lens and examine the
statistics of gravitational lensing by a population of virialized and
non-virialized structures using sub-mm galaxies at z ~ 2.6 and Lyman-break
galaxies at redshifts z ~ 6 - 15 as the background sources. We quantify the
effect of lensing on the luminosity function of the high redshift sources,
focusing on the intermediate and small magnifications, mu < 2, which affect the
majority of the background galaxies, and comparing to the case of strong
lensing. We show that, depending on the intrinsic properties of the background
galaxies, gravitational lensing can significantly affect the observed
luminosity function even when no obvious strong lenses are present. Finally, we
find that in the case of the Lyman-break galaxies it is important to account
for the surface brightness profiles of both the foreground and the background
galaxies when computing the lensing statistics, which introduces a selection
criterion for the background galaxies that can actually be observed. Not taking
this criterion into account leads to an overestimation of the number densities
of very bright galaxies by nearly two orders of magnitude.
