From a rediscussion of Local Group membership , and of distances to individual galaxies , we obtain M _ { V } values for 35 probable and possible Local Group members .
The luminosity function of these objects is well fitted by a Schechter function with faint end slope \alpha = -1.1 \pm 0.1 .
The probability that the luminosity distribution of the Local Group is a single Schechter function with \alpha steeper than -1.3 is less than 1 per cent .
However , more complicated luminosity functions , such as multi-component Schechter functions with steep faint-end slopes , can not be ruled out .
There is some evidence that the luminosity distribution of dwarf spheroidal galaxies in the Local Group is steeper than that of dwarf irregular galaxies .