Introduction to Ergodic Theory

1. Measure preserving systems for Borel group actions
2. Ergodicity, ergodic decomposition, mixing and weak mixing
3. Minimality and unique ergodicity
4. Mean and pointwise ergodic theorems for a single transformation
5. (*) Joinings
6. (*) Decomposition of a measure relative to a partition and conditional measures
7. (*) Entropy
8. (*) Ergodic theorems for general groups and amenability.

(*) denotes optional topics to be covered according to class level and teacher discretion.