Lectures on the Entropy Theory of Measure-Preserving Transformations

CONTENTS Introduction § 1. Preliminaries from measure theory § 2. Isometric operators § 3. Measure-preserving transformations § 4. Entropy of a measurable partition § 5. Mean conditional entropy § 6. Spaces of partitions § 7. Fundamental lemmas § 8. Properties of the function h(T, ξ) § 9. Entropy of an endomorphism § 10. Existence of generators § 11. Automorphisms with zero entropy § 12. The theory of invariant partitions § 13. Endomorphisms with completely positive entropy § 14. Entropy and the spectrum § 15. Entropy and mixing § 16. Entropy and the isomorphism problem Appendix. S. A. Yuzvinskii, Metric properties of endomorphisms of locally-compact groups References