Upper panel: function of the comoving volume between redshift 0.51 and z, filled by either HD and LD regions (violet and orange lines). The function is evaluated by means of a Monte Carlo integration as described in the text. To find the V_max of a galaxy, one has to consider the volume between its minimum and maximum allowed redshift (z_min and z_min, see the vertical dashed lines as an example). Lower panel: the fraction of the total volume (between z = 0.5 and the given redshift) occupied by HD and LD regions (violet and orange lines).