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 \simeq 2 since z \simeq 1 if q _ { 0 } = 0.0 or by factor \simeq 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 .