How is the theory of ergodic measure-preserving transformations related to ergodicity in the physical sense (which I understood as, very very roughly speaking, that a physical system is called ergodic if "averaging" over "states" of the physical system equals the "average" over time)?
I am sorry maybe the question is a bit unspecific for now, but I guess it's still of interest also for others who are about to dive into the subject.