Measure & Ergodic Theory

These are the course notes for the Autumn 2023 course Math 41021 Measure Theory and Ergodic Theory. Some background material is available.

  1. Length
  2. σ-algebras
  3. Measurable functions
  4. Measures
  5. Constructing measures
  6. Integration
  7. Lebesgue spaces
  8. Representing measures
  9. Introduction to dynamics
  10. Uniform distribution
  11. Full shifts
  12. The law of large numbers
  13. Measure preserving maps
  14. Ergodicity
  15. The ergodic theorem
  16. Normal numbers
  17. The Koopman operator
  18. Fourier series
  19. Entropy
  20. Markov chains