Index 337 monad, 267 Newman’s first theorem, 291 Newman’s second theorem, 292 nilpotent Lie algebra, 251 nilprogression, 165 nilradical, 257 no small subgroups, 106 noncommutative progression, 18, 165 nonstandard finite set, 158 nonstandard function, 152 nonstandard object, 149 nonstandard space, 149 nonstandard universe, 149 normal Sanders lemma, 182 normal sub-local group, 119 normalising neighbourhood, 119 notation, xii NSS, 106 NSS approximate group, 208 one-parameter subgroup, 41, 57 open mapping theorem, 56 orthogonal group, 9 outer regularity, 77 overspill principle, 155 periodic group, 233 Peter-Weyl theorem, 298 Plancherel identity, 303 Poincar´ e-Birkhoff-Witt theorem, 250 pointed Gromov-Hausdorff convergence, 174 pointed metric space, 174 probability space, 313 profinite group, 130, 134 projective limit, 93 pseudometric, 100 pushforward, 32 quotient space, 120 quotiented commutator map, 242 radially homogeneous C1,1 local group, 39 radical, 255 Radon measure, 77 regular representation, 74, 88 restricted Burnside problem, 235 restriction of a local group, 27 Riesz lemma, 64 Riesz representation theorem, 78 Ruzsa covering lemma, 183 Ruzsa triangle inequality, 221 Sanders lemma, 168, 212 Schur’s lemma, 298 Schur’s theorem, 233 smooth action, 87 smooth atlas, 8 smooth manifold, 8 smooth structure, 8 soft analysis, 139 solenoid, 12 special orthogonal group, 9 special unitary group, 9 spectral theorem, 90 stabiliser subgroup, 86 standard function, 152 standard object, 148 standard part, 159 standard universe, 148 Stone-Cech compactification, 146 strictly nonstandard, 150 sub-local group, 119 subgroup trapping, 112, 122 submanifold, 54 syndetic set, 95 tangent bundle, 31 tangent space, 30 tangent vector, 31 Tonelli theorem, 319 topological group, 10 topological manifold, 8 topological vector space, 61 torsion group, 162 totally disconnected space, 128 transitive action, 86, 127 triangle removal lemma, 315, 321 ultra approximate group, 162, 212 ultrafilter, 145 ultralimit, 149 ultrapower, 149 ultraproduct, 149 uniform total boundedness, 172 uniqueness of Lie structure, 42 unitary group, 9 universal cover, 226 universal enveloping algebra, 249 van Dantzig’s theorem, 128 vector field, 32 von Neumann’s theorem, 54
Previous Page Next Page