all the LFs have been calculated selecting the stars within $2.5\sigma$ (again, $\sigma$ is the standard deviation of the mean color) from the fiducial line of the main sequence of the cluster. The LFs do not include the HB and BS stars. The LF of the background stars has a particular shape: it suddenly drops at $M_V=4.0$. This feature has a natural explanation considering the color-magnitude distribution of the field stars around M55 and the way we selected the stars. The drop in the number of field stars is at the level of the M55 TO and as can be seen in Figure \[M55tot\], or in the lower right panel in Figure \[cmdradial\], the TO of M55 is bluer than the TO of the halo stars of the Galaxy, which are the main components of the field stars towards M55 [@Mand96]. Selecting only stars within $2.5\sigma$ of the fiducial line of M55 will naturally cause such a drop.

The completeness correction, as obtained in appendix \[crowd\], has been applied to the stellar counts of each field of M55. As it is possible to see from Table \[M55tab2\], the magnitude limit varies from field to field. We have adopted the same, 