Mattig's relation and dynamical distance indicators
  We discuss how the redshift (Mattig) method in Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is the distance itself (in this case the proper metric distance). As the Friedmann model has Newtonian analogy, its use to infer distances has instructive similarities to classical dynamical distance indicators. In view of the theoretical exact linear distance-velocity law, we emphasize that it is conceptually correct to derive the cosmological distance via the route: redshift (primarily observed) --> space expansion velocity (not directly observed) --> metric distance (physical length in "cm"). Important properties of the proper metric distance are summarized. 
Pekka Teerikorpi and Yurij Baryshev
gr-qc astro-ph.CO