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