have tested our combining procedure in several ways. In one of our tests we built LFs of two EMMI fields at the same distance from the center of the cluster: , we compared the LF of the field 2 with that of the field 6. After having corrected for the ratio between the covered areas and subtracting the field star contribution, the two LFs were consistent in all the magnitude intervals down to the completeness level of the data (that is lower than the one adopted). Having for field 2 a magnitude limit of 22.2 (see Table \[M55tab2\]) and field 6 a limit of 21.5, we also verified that for the latter our star counts are in correct proportion below the completeness level of 50%.

In a second test, we generated two LFs dividing the whole cluster in two octants (dividing along the $45^\circ$ line that runs from the center of the cluster till the field 19  Figure \[M55frames\]). For each of the two slices we generated three LFs in the same radial range as in Figure \[M55fdl\]. After comparing all of them we did not find any significant difference. Therefore the differences among the three LFs in Figure \[M55fdl\] 