Ergodic theory (Ancient Greek: ergon work, hodos way) is a branch of mathematics that studies dynamical systems with an Invariant measure (intuitively, the stationary distribution) and related problems

An

Ergodic Theory - Stefano Luzzatto - Lecture 01. Introduction to Measure theory, and Probability theory

https://en.wikipedia.org/wiki/Ergodic_theory

Recent Trends in Ergodic Theory and Dynamical Systems

Karma Dajani - An introduction to Ergodic Theory of Numbers (Part 1)

(ML 18.2) Ergodic theorem for Markov chains

http://mathoverflow.net/questions/82661/book-recommendation-for-ergodic-theory-and-or-topological-dynamics