Peculiar velocity measurement in a clumpy universe
  In this work we address the issue of peculiar velocity measurement in a
perturbed Friedmann universe using the deviations from measured luminosity
distances of standard candles from background FRW universe. We want to show and
quantify the statement that in intermediate redshifts ($0.5< z < 2$),
deviations from the background FRW model are not uniquely governed by peculiar
velocities. Luminosity distances are modified by gravitational lensing. We also
want to indicate the importance of relativistic calculations for peculiar
velocity measurement at all redshifts.
  For this task we discuss the relativistic correction on luminosity distance
and redshift measurement and show the contribution of each of the corrections
as lensing term, peculiar velocity of the source and Sachs-Wolfe effect. Then
we use the SNe Ia sample of Union 2, to investigate the relativistic effects we
consider.
  We show that, using the conventional peculiar velocity method, that ignores
the lensing effect, will result in an overestimate of the measured peculiar
velocities at intermediate redshifts. Here we quantify this effect. We show
that at low redshifts the lensing effect is negligible compare to the effect of
peculiar velocity. From the observational point of view, we show that the
uncertainties on luminosity of the present SNe Ia data prevent us from precise
measuring the peculiar velocities even at low redshifts ($z<0.2$).
