Index
B(G), 205
B(X Y ), 128
BC(X Y ), 112
C(X Y ), 112
C∗
algebra, 154
C0
∞(Rd),
213
Cc
∞(Rd),
213
Ck(Rd),
238
Ck,α(Rd),
240
Cc(X R), 136
Hs(Rd),
251
L0
norm, 39
M(X), 148
W k,p(Rd), 243
σ-compact, 75, 78
σ-finite, 6
c0(N), 62
cc(N), 62
z-transform, 208
Absolute value of a measure, 20
Absolutely continuous component, 21
Absolutely continuous measure, 21
Absolutely integrable function, 10
Abstract Boolean algebra, 293
Adherent point, 72, 77
Adjoints (Hilbert spaces), 54
Alexander subbase theorem, 106
Algebraic Hahn-Banch theorem, 70
Algebraic topology, 120
Almost everywhere, 7
Almost open, 87
Almost surely, 7
Amenable group, 285, 335
Approximation to the identity, 216
Arzel´ a-Ascoli diagonalisation argument,
109
Arzel´ a-Ascoli theorem, 114
Axiom of choice, 301
Baire category theorem, 86
Baire set, 87
Banach ∗-algebra, 192
Banach algebra, 154
Banach space, 36
Banach-Alaoglu theorem, 126
Banach-Mazur theorem, 67
Banach-Schr¨ oder-Bernstein theorem,
283
Banach-Steinhaus theorem, 89
Banach-Tarski paradox, 292
Base (topology), 104
Basic open neighbourhood, 104
Bessel inequality, 55
Beurling-Gelfand spectral radius
formula, 155
Birkhoff’s representation theorem, 297
Bochner’s theorem, 205
Bolyai-Gerwien theorem, 290
Boolean algebra, 293
Boolean algebra morphism, 295
Borel σ-algebra, 4
Borel measurable, 4
Bounded set, 73
Box topology, 108
345
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