We have analysed the proper motion data of LHS catalog, to derive the faint end of the luminosity function more precise than ever before, by mean absolute method, and by making use of the reudced proper motion diagram. It is found that the relations between the mean absolute magnitude and the reduced proper motion for main sequence stars, subdwarfs, and white dwarfs are so different that the proper application of an appropriate relation to each group is much more important. The derived luminosity function shows the broad maximum peak from M B ∼ 14 to M B ∼ 17 and declines after M B ∼ 17 up to M B ∼ 22 .

Combining the luminosity functions of main sequence stars in 3 associations and 22 open clusters, the initial luminosity function and mass function for these clusters are derived. For stars of m > 0.6 m ⊙ , they are well consistent with those for the field stars.

188 galactic clusters have been investigated to obtain their luminosity functions. It is attempted to interpret the resulting luminosity functions in regard to cluster formation.