Proving the conservation of surface brightness during the strong and   weak lensing of light by an isothermal sphere
  An analytical proof of the conservation of surface brightness during the strong and weak lensing of light by a singular isothermal sphere is provided. It is shown that the movement of asymptotic rays provide room for precisely the extra solid angle claimed by the magnification of the centrally passing rays. Previous claim of a violation of this conservation law, leading to a problem over the COBE all sky CMB flux, is hereby withdrawn. 
Richard Lieu