Rest-frame FUV 1 / V_max LF data points for the Deep survey (cyan empty squares) and the Ultra-Deep survey (blue filled triangles), from z = 0.05 to z = 4.50. There is no Ultra-Deep data in the lowest redshift bin. In each panel, the FUV absolute magnitude LF bias limit (see Sect. 3.1) is shown as a vertical cyan long-dashed line for the Deep survey and as a blue short-dashed line for the Ultra-Deep survey. The number quoted in parenthesis is the total number of used galaxies. We overplot the STY determinations of the merged Deep+Ultra-Deep sample, as illustrated in Fig. 1 and tabulated in Table B.1): (i) with free Schechter parameters (solid lines) and its associated error (shaded area), (ii) in setting the faint-end slope at z > 1.7 (dashed lines), and (iii) in setting at z < 0.2 (dashed line) and reported as a reference in the z > 0.2 panels (dotted lines).