Is this invariance assuming perfect ray transportation (vacuum, for example)? In previous lectures, the intensity of light is assumed to decrease exponentially with distance from source.
^I believe since the way we measure rays of light is through radiance', it doesn't change through distance. Also, there are probably assumptions and shortcuts baked in for it to make more sense and be easy to apply. Though the most important principle from this is lighting originating from intersection points with antiparallel rays have the same radiance.
I think it's tricky to apply the invariance of radiance along rays here. In general, incident and exitant radiance are different since materials absorb part of the energy of the incident light. The invariance here seems to show that the loss of radiance converges after many iterations of reflection and thus incident and exitant radiance approaches an equality.
I think the rule of radiance invariance along rays is like the preservation of the radiance. We find out the amount of the source radiance. And at every point, the radiance should be same.