Weak lensing measurement of the mass-richness relation using the SDSS
  database
  We study the mass-richness relation using galaxy catalogues and images from
the Sloan Digital Sky Survey. We use two independent methods, in the first one,
we calibrate the scaling relation with weak-lensing mass estimates. In the
second procedure we apply a background subtraction technique to derive the
probability distribution, $P(M \mid N)$, that groups with $N$-members have a
virialized halo mass $M$. Lensing masses are derived in different richness bins
for two galaxy systems sets: the maxBCG catalogue and a catalogue based on a
group finder algorithm developed by Yang et al. MaxBCG results are used to test
the lensing methodology. The lensing mass-richness relation for the Yang et al.
group sample shows a good agreement with $P(M \mid N)$ obtained independently
with a straightforward procedure.
