I'm trying to understand ergodic theorems. I use the book written by Peter Walters "An introduction to ergodic theorem".
I would like to ask what would one consider to be an ergodic theorem for discrete time and ergodic theorem for continuous time?
I also would like to know what was the first ergodic theorem? I would like to understand the proofs chronologically. Maybe there is a really simple paper of book containing those?
I would really appreciate any hints or tips.