Real and Complex Analysis (Rudin)

INDEX 415
Separable space, 92, 247
Set, 6
Borel,13
closed, 13, 35
compact, 36
connected, 196
convex, 79
dense, 58
elementary, 161
empty, 6
F., 12
G,,12
inner regular, 47
measurable, 8, 51
nonmeasurable, 53, 157, 167
open, 7
outer regular, 47
partially ordered, 86
strictly convex, 112
totally disconnected, 58
totally ordered, 87
Shift operator, 347
Sierpinski, W., 167,399
a-algebra, 8
a-compact set, 47
a-finite measure, 47
a-ring, 397
Signed measure, 119
Simple boundary point, 289
Simple function, 15
Simply connected, 222, 274
Sine, 2, 265, 316
Singer, I. M., 398, 402
Singular measure, 120
Singular point, 319
Snow, D.O., 399
Space:
Banach,95
compact, 35
complete metric, 67
dual, 108, 112, 127, 130
Hausdorff, 36
Hilbert, 77
inner product, 76
locally compact, 36
measurable, 8
metric, 9
normed linear, 95
separable, 92
topological, 8
unitary, 76
vector, 33
Span, 82
Spectral norm, 360
Spectral radius, 360
Spectrum, 357
Square root, 274
Stoilov's theorem, 400
Stout, E. L., 401
Strictly convex set, 112
Stromberg, K., 399
Subadditivity, 397
Subchain, 395
Subharmonic function, 335
Subset, 6
Subspace, 78
Sum of paths, 217
Summability method, 114
Summable function, 24
Supremum, 7
Supremum norm, 70
Support, 38, 58
Symmetric derivative, 136
Szasz, 0., 401
Tauberian theorem, 402
Taylor's formula, 379
Thorin, G. 0., 401
Three-circle theorem, 264
Tietze's extension theorem, 389
Topological space, 8
Topology, 8
Total variation, 117, 148
Totally disconnected set, 58
Totally ordered set, 87
Tower, 395
Transcendental number, 170
Transformation:
affine, 377
bounded linear, 96
differentiable, 150
linear, 33
linear fractional, 279, 296
(See also Function)
Transitivity, 324
Translate:
offunction, 182
of set, 50
Translation-invariance, 51
Translation-invariant measure, 51
Translation-invariant subspace, 188
Triangle, 202
Triangle inequality, 9, 49, 77
Trigonometric polynomial, 88
Trigonometric system, 89
Ullrich, D., 400
Uniform boundedness principle, 98