The galaxy luminosity function and the redshift-distance controversy (A Review).

The mean relation between distance and redshift for galaxies is reviewed as an observational question. The luminosity function for galaxies is an important ingredient and is given explicitly. We discuss various observational selection effects that are important for comparison of the linear and quadratic distance-redshift laws. Several lines of evidence are reviewed, including the distribution of galaxy luminosities in various redshift ranges, the luminosities of brightest galaxies in groups and clusters at various redshifts, and the Tully-Fisher correlation between neutral hydrogen velocity widths and luminosity. All of these strongly favor the linear law over the quadratic.