336 Index
edge density, 314
elementary set, 322
equivariant map, 298
escape norm, 201
existence and uniqueness of Haar
measure, 78
exponential coordinates, 41
exponential map, 69
extension problem, 277
faithful action, 127
finite trapping, 114
formal commutator word, 243
formal predicate, 157
Fourier analysis on compact abelian
groups, 94
Fourier inversion formula, 303
Freiman’s theorem, 17, 164
Fubini-Tonelli theorem, 314
gauge transformation, 281
general linear group, 9
generalised arithmetic progression, 16,
164
Gleason lemma, 202
Gleason metric, 55
Gleason-Yamabe theorem for abelian
groups, 96
Gleason-Yamabe theorem for compact
groups, 92
good model, 185, 213
Gromov’s theorem, 21, 224
Gromov-Hausdorff distance, 171
group cohomology, 281
group germ, 267
group of polynomial growth, 21
Haar measure, 77, 87
Hadamard lemma, 46
half-open topology, 62
Hall-Witt identity, 240
hard analysis, 139
Hausdorff distance, 116, 170
height, 308
Heisenberg group, 9
Helfgott-Lindenstrauss conjecture, 216
Hilbert’s fifth problem, 10, 133
Hilbert-Smith conjecture, 289
homogeneous space, 86
homomorphism, 29
Hrushovski Lie model theorem, 213
Hrushovski’s Lie model theorem, 192,
195
Hrushovski’s structure theorem, 194
hyperreal, 149
indicator function, xiii
infinitesimal, 159
infinitesimal part, 159
inner regularity, 77
internal function, 152
internal set, 149
invariance of dimension, 126
invariance of domain, 126, 132
inverse limit, 93
irreducible representation, 298
isotypic component, 300
Jacobi identity, 249
Jordan’s theorem, 6, 233
Jordan-Schur theorem, 233
Keisler-Fubini theorem, 319
lamplighter group, 191
left-invariant vector field, 34
Leibniz rule, 33
Levi’s theorem, 258
Lie algebra, 33
Lie algebra of a Lie group, 34
Lie bracket, 33
Lie group, 8
Lie groups are analytic, 49
Lie’s first theorem, 40
Lie’s second theorem, 50
Lie’s third theorem, 35, 50, 270
lifting lemma, 215
local finiteness, 77
local Gleason metric, 121
local Gleason-Yamabe theorem, 121
local group, 26
local Haar measure, 86
local homomorphism, 29
local Lie group, 27
Local Lie implies Lie, 43
local section, 283
local topological group, 26
Loeb measure, 317
Los’s theorem, 154
lower central series, 241
Margulis-type lemma, 229
matrix exponential, 4
measure space, 313
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