  The K-band Hubble diagram for a sample of brightest cluster galaxies (BCGs)
in the redshift range 0<z<1 shows a very small scatter (0.3 magnitudes r.m.s).
The BCGs exhibit very little luminosity evolution in this redshift range: if
q_0=0.0 we detect no luminosity evolution; for q_0=0.5 we measure a small
negative evolution. If the mass in stars of these galaxies had remained
constant over this period of time, substantial positive luminosity evolution
would be expected: BCGs should have been brighter in the past since their stars
were younger. This suggests that the stellar mass of the BCGs has been
assembled over time through merging and accretion. We estimate that the stellar
mass in a typical BCG has grown by a factor ~ 2 since z=1 if q_0=0.0 or by
factor ~ 4 if q_0=0.5. These results are in remarkably good agreement with the
predictions of semi-analytic models of galaxy formation and evolution set in
the context of a hierarchical scenario for structure formation.
