 -algebra 3
Affine transformation 18
Aperiodic 89
Bernoulli shift 18 98
Character theory 10
Complete invariant 96
Completely positive entropy 104
Conditional entropy 76
Conjugate transformations 53
Continuous spectrum 46
Direct product of probability spaces 5
Direct product of transformations 44
Discrete spectrum, measure theoretic 64
Discrete spectrum, topological 125
Distal 120
Eigenfunction, measure theoretic 45 63
Eigenfunction, topological 123
Eigenvalue, measure theoretic 45
Eigenvalue, topological 123
Endomorphisms of tori 12
entropy 7 2
Entropy of affine transformations of tori 168
Entropy of Bernoulli shifts 95
Entropy of rotations 93
Ergodic theorem,  3 6
Ergodic theorem, Birkoff 29
Ergodic theorem, maximal 32
Ergodicity 21
Exact endomorphism 111
Expansive homeomorphism 171
Generator, measure-theoretic 88
Generator, topological 168
Haar measure 9
Hahn — Kolmogorov extension theorem 4
Hilbert spaces 8
Induced operator on 32
Invariant 57
Invariant measures for homeomorphisms 128
Isomorphism 52
Kolmogorov automorphism 101
| Kolmogorov — Sinai theorem 87
Krylov and Bogolioubov Theorem 132
Lebesgue Covering Lemma 151
Lebesgue spectrum 60
Markov chain 105
Measure algebra 53
Measure preserving transformation 16
Measure theory 3
Minimal homeomorphism 113
Minimal set 114
Mixing 37
Nilmanifold 106
Non-invertible transformation 110
Normal number 31
Orbit 113
Partitions 70
Periodic point 115
Pinsker algebra 107
Poincare recurrence theorem 20
Pure point spectrum 64
Recurrence 20
Refinement of open covers 140
Riesz representation theorem 130
Rotations on groups 67
Semi-simple homeomorphism 115
Separated set 146
Sequence entropy 108
Spanning set 146
Spectral isomorphism 54
Spectral theorem 46
Sub--algebras 70
Topological conjugacy 122
Topological entropy 143 147
Topological entropy of affine transformations of tori 168
Topological entropy of Bernoulli shifts 182
Topological entropy of homeomorphisms of the circle 182
Topological entropy, connection with measure theoretic entropy 155
Topological transitivity 117
Uniformly equivalent metrics 150
Uniquely ergodic 135
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