INDEX 237
realizable by an action, 220
realized, 208
recurrent, 140, 145
reduction, 136
reduction cocycle, 138, 139
relative property (T), 115
residually amenable, 27
residually finite, 27
restricted multiplicity, 38
Rokhlin property, 93
Schur’s Lemma, 210
semidirect product, 223
shift action, 46
skew product action, 69
smooth, 28, 138, 139
somewhere cocycle superrigid, 162
spectral measure, 200
spectral rigidity, 93
spectrally equivalent, 7, 66
stabilizer, 131
stabilizer of the action, 47
stable, 56
standard measure space, 1
strict cocycle, 129, 131
strong operator topology, 187
strong topology, 207
strongly ergodic, 32, 62
strongly treeable, 55, 186
subrepresentation, 95
symmetric difference, 1
symmetric Fock space, 190
symmetric tensor power, 189
topological ergodic decomposition, 65
topological generator, 26
topologically locally finite, 6
transient, 140
translation part, 223
treeable, 52
trivial cocycle, 130
trivial one-dimensional representation,
79
turbulent, 30, 45
Uniform Approximation Theorem, 6, 14
uniform topology, 3
unitarily equivalent, 7, 66
unitary equivalence, 95
variety, 107
Weak Approximation Theorem, 5
weak mixing, 10, 62, 217
weak operator topology, 187
weak topology, 1, 207
weakly commutative groups, 53
weakly contained, 64, 208
weakly contained in the sense of
Zimmer, 209
weakly equivalent, 64, 131, 208
weakly isomorphic, 69
Wick product, 193
Wiener chaos decomposition, 193
witness the weak commutativity, 56
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