Real and Complex Analysis (Rudin)

410 INDEX
Cartesian product, 7,160
Category theorem, 98
Cater, F. S., 398
Cauchy, A., 400
Cauchy formula, 207, 219, 229, 268, 341, 384,
388
Cauchy-Riemann equations, 232
Cauchy sequence, 67
Cauchy theorem, 205, 206, 207, 218
Cauchy's estimates, 213
Cell, SO
Chain, 218
Chain rule, 197
Change of variables, 153, 156
Character, 179
Characteristic function, 11
Choice function, 396
Class, 6
Closed curve, 200
Closed graph theorem, 114
Closed path, 201
Closed set, 13, 35
Closed subspace, 78
Closure, 35
Cohen, P. J., 402
Collection, 6
Commutative algebra, 356
Commutative law, 18
Compact set, 35
Complement, 7
Complete measure, 28
Complete metric space, 67
Completion:
of measure space, 28, 168
of metric space, 70, 74
Complex algebra, 356
Complex field, 213, 359
Complex homomorphism, 191,362
Complex-linear functional, 105
Complex measure, 16, 116
Complex vector space, 33
Component, 197
Composite function, 7
Concentrated, 119
Conformal equivalence, 282
Conjugate exponents, 63
Conjugate function, 3SO
Connected set, 196
Continuity, 8, 9
Continuous function, 8
Continuous linear functional, 81, 96, 113, 127,
130
Continuous measure, 175
Continuum hypothesis, 167
Convergence:
dominated, 26
in IJ, 67
in measure, 74
monotone, 21
almost uniform, 214
uniform on compact subsets, 214
weak,245
Convex function, 61
Convex sequence, 410
Convex set, 79
Convexity theorem, 257
Convolution, 170, 175, 178
Coset, 362
Cosine, 2, 265
Countable additivity, 6,16
Counting measure, 17
Cover, 35, 324
Covering lemma, 137,399
Curve, 200
with orthogonal increments, 94
Cycle, 218
Daniell, P. J., 398
de Branges, L., 401
Denjoy, A., 144
Denjoy-Carleman theorem, 380
Dense set, 58
Derivative, 135, 197
of Fourier transform, 179
of function of bounded variation, 157
of integral, 141
of measure, 136, 142, 143, 241
symmetric, 136
of transformation, ISO
Determinant, 54
Diagonal process, 246
Dieudonne, J., 398
Differentiable transformation, 150
Differential, ISO
Direct continuation, 323
Dirichlet kernel, 101
Dirichlet problem, 235
Disc,9,196
Discrete measure, 175
Disjoint sets, 7
Distance function, 9
Distribution function, 172
Distributive law, 18
Division algebra, 360.
Dixon, J. D., 400
Domain, 7
Dominated convergence theorem, 26, 29,
180