Problem Sheet C
- Problem 1 gives a bunch more equivalent ways of formulating the weakly mixing property using two or three sets. (Compare to Proposition 5.13.)
- Problem 2 is (yet) another cute characterisation of weakly mixing systems.
- Problem 3 introduces the notion of totally transitive systems, and asks you to prove that weakly mixing $ \Rightarrow$ totally transitive, and that totally transitive + chaotic $ \Rightarrow $ weakly mixing.
- Problem 4 is fun (and harder than it looks).
Comments and questions?