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