Description
Book SynopsisChapter 1. Preliminaries.- Part I. The Fundamentals.- Chapter 2. Measure-preserving systems.- Chapter 3. Minimality and ergodicity.- Chapter 4. Some Fourier analysis.- Chapter 5. The spectral theorem.- Chapter 6. Decompositions in Hilbert spaces.- Part II. Classical Ergodic Theorems.- Chapter 7. Classical ergodic theorems and more.- Chapter 8. Factors of measure-preserving systems.- Chapter 9. First applications of ergodic theorems.- Chapter 10. Equidistribution.- Chapter 11. Groups, semigroups and homogeneous spaces.- Part III. More Ergodic Theorems.- Chapter 12. Subsequential ergodic theorems.- Chapter 13. Multiple recurrence.- Chapter 14. Nilsystems.- Chapter 15. Gowers–Host–Kra seminorms and multiple convergence.- Chapter 16. Weighted ergodic theorems.- Chapter 17. Sarnak’s conjecture.
