Time and Place:
- Measure preserving systems for Borel group actions
- Ergodicity, ergodic decomposition, mixing and weak mixing
- Minimality and unique ergodicity
- Mean and pointwise ergodic theorems for a single transformation
- (*) Joinings
- (*) Decomposition of a measure relative to a partition and conditional measures
- (*) Entropy
- (*) Ergodic theorems for general groups and amenability.
(*) denotes optional topics to be covered according to class level and teacher discretion.