| Preface | p. ix |
| Introduction and preliminaries | p. 1 |
| The basic questions of ergodic theory | p. 1 |
| The basic examples | p. 5 |
| Hamiltonian dynamics | |
| Stationary stochastic processes | |
| Bernoulli shifts | |
| Markov shifts | |
| Rotations of the circle | |
| Rotations of compact abelian groups | |
| Automorphisms of compact groups | |
| Gaussian systems | |
| Geodesic flows | |
| Horocycle flows | |
| Flows and automorphisms on homogeneous spaces | |
| The basic constructions | p. 10 |
| Factors | |
| Products | |
| Skew products | |
| Flow under a function | |
| Induced transformations | |
| Inverse limits | |
| Natural extensions | |
| Some useful facts from measure theory and functional analysis | p. 13 |
| Change of variables | |
| Proofs by approximation | |
| Measure algebras and Lebesgue spaces | |
| Conditional expectation | |
| The Spectral Theorem | |
| Topological groups, Haar measure, and character groups | |
| The fundamentals of ergodic theory | p. 23 |
| The Mean Ergodic Theorem | p. 23 |
| The Pointwise Ergodic Theorem | p. 27 |
| Recurrence | p. 33 |
| Ergodicity | p. 41 |
| Strong mixing | p. 57 |
| Weak mixing | p. 64 |
| More about almost everywhere convergence | p. 74 |
| More about the Maximal Ergodic Theorem | p. 74 |
| Positive contractions | |
| The maximal equality | |
| Sign changes of the partial sums | |
| The Dominated Ergodic Theorem and its converse | |
| More about the Pointwise Ergodic Theorem | p. 90 |
| Maximal inequalities and convergence theorems | |
| The speed of convergence in the Ergodic Theorem | |
| Differentiation of integrals and the Local Ergodic Theorem | p. 100 |
| The Martingale convergence theorems | p. 103 |
| The maximal inequality for the Hilbert transform | p. 107 |
| The ergodic Hilbert transform | p. 113 |
| The filling scheme | p. 119 |
| The Chacon-Ornstein Theorem | p. 126 |
| More about recurrence | p. 133 |
| Construction of eigenfunctions | p. 133 |
| Existence of rigid factors | |
| Almost periodicity | |
| Construction of the eigenfunction | |
| Some topological dynamics | p. 150 |
| Recurrence | |
| Topological ergodicity and mixing | |
| Equicontinuous and distal cascades | |
| Uniform distribution mod 1 | |
| Structure of distal cascades | |
| The Szemeredi Theorem | p. 162 |
| Furstenberg's approach to the Szemeredi and van der Waerden Theorems | |
| Topological multiple recurrence, van der Waerden's Theorem, and Hindman's Theorem | |
| Weak mixing implies weak mixing of all orders along multiples | |
| Outline of the proof of the Furstenberg-Katznelson Theorem | |
| The topological representation of ergodic transformations | p. 186 |
| Preliminaries | |
| Recurrence along IP-sets | |
| Perturbation to uniformity | |
| Uniform polynomials | |
| Conclusion of the argument | |
| Two examples | p. 209 |
| Metric weak mixing without topological strong mixing | |
| A prime transformation | |
| Entropy | p. 227 |
| Entropy in physics, information theory, and ergodic theory | p. 227 |
| Physics | |
| Information theory | |
| Ergodic theory | |
| Information and conditioning | p. 234 |
| Generators and the Kolmogorov-Sinai Theorem | p. 243 |
| More about entropy | p. 249 |
| More examples of the computation of entropy | p. 249 |
| Entropy of an automorphism of the torus | |
| Entropy of a skew product | |
| Entropy of an induced transformation | |
| The Shannon-McMillan-Breiman Theorem | p. 259 |
| Topological entropy | p. 264 |
| Introduction to Ornstein Theory | p. 273 |
| Finitary coding between Bernoulli shifts | p. 281 |
| Sketch of the proof | |
| Reduction to the case of a common weight | |
| Framing the code | |
| What to put in the blanks | |
| Sociology | |
| Construction of the isomorphism | |
| References | p. 302 |
| Index | p. 322 |
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