In this lecture we discuss a “functional analytic” interpretation of mixing and weakly mixing for measure-preserving dynamical systems.

The last part of this lecture is non-examinable, since it uses a version of the Spectral Theorem that you probably have not seen before[1].

Next lecture we will move back into the topological world, and investigate when[2] a topological dynamical system on a compact metric space admits an invariant measure (i.e. a measure for which the system becomes measure-preserving).

  1. If you have not seen the Spectral Theorem in this form before, I recommend Rudin's book Functional Analysis. ↩︎

  2. Spoiler: Always. ↩︎

Comments and questions?