236 INDEX
cohomology group, 130, 132, 224
cohomology space, 130, 132, 224
complexification, 187
Conjugacy Lemma, 6, 14
conjugacy shift action, 55
conjugate, 133
conjugate representation, 219
contained, 208
Continuum Hypothesis, 155
convergence in measure, 126
cost, 75
countable equivalence relation, 13
counting measure, 129
cyclic dyadic permutation, 5
cyclic vector, 199
densely representable, 216
Dirichlet sets, 11
dyadic permutation, 5
Effros’ Theorem, 144
equivalent cocycles, 130, 132
equivalent measures, 35
ergodic, 62, 217
ergodic equivalence relation, 13
essential range, 141
factor, 69
finite equivalence relation, 13
finite factors, 175
first chaos, 193
fixed price, 75
free action, 25
full group, 13
Gaussian centered measure, 191
Gaussian Hilbert spaces, 193
Gaussian shift, 192
Haagerup Approximation Property, 79
homomorphism, 68
hyperfinite equivalence relation, 18
independent set, 37
induced action, 74, 203
induced representation, 203
induced transformation, 12
infinite conjugacy classes, 52
inner amenable, 52
inner automorphism group, 13
intertwining operator, 210
irreducible, 210
isomorphic, 20, 61, 207
isomorphism, 95
isomorphism cocycle, 140
join, 99
joining, 65
Kazhdan pair, 85
kernel, 137
Koopman representation, 2, 66
locally closed, 212
locally topologically finitely generated,
27
Mackey action, 137, 139
Mackey range, 137, 139
malleable, 184
marginal, 65
maximal spectral type, 200
measure algebra, 1
measure preserving equivalence relation,
13
measure-hyperfinite, 176
mild mixing, 10, 62, 217
minimal condition on centralizers, 168
minimally almost periodic, 83
mixing, 10, 62, 217
mixing representation, 79
multiplicative operators, 2
Mycielski, Kuratowski Theorem, 18
negative-definite, 82
non-0 almost invariant vectors, 79
non-trivial asymptotically invariant
sequence, 57
orbit equivalence cocycle, 140
orbit equivalent, 57, 62
orthogonal group, 187
outer automorphism group, 44
periodic, 5
periodic equivalence relation, 13
Poincar´ e flow, 137, 139
positive-definite function, 191, 192, 199
positivity preserving operators, 2
product action, 65
projection valued measure, 199
property (FD), 219
property (M), 83
property (S), 83
property (T), 81
property (W), 83
Rajchman measure, 36
realification, 187
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