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Rudin W. — Real and Complex Analysis
Rudin W. — Real and Complex Analysis



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Название: Real and Complex Analysis

Автор: Rudin W.

Аннотация:

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 412

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$F_{\sigma}$-set      12
$G_s$-set      12
$\pi$      3
$\sigma$-algebra      8
$\sigma$-compact set      47
$\sigma$-finite measure      47 124 138 140
Absolute continuity      121 125 159 335
Absolute continuity of functions      165
Absolute convergence      117
Absolutely convergent Fourier series      363
Addition formula      1
Affine transformation      373
Ahlfors, L. V.      398
Algebra      351
Algebra of measures      149
Algebra of sets      10
Algebraically closed field      218
Almost everywhere      27
Almost uniform convergence      214
Analytic continuation      316 372.
Analytic function      199
Annulus      249 266 282 286
Area      221
Area theorem      277
Arens, R.      394
Argument      205
Arithmetic mean      62 91 94
Associative law      192
Asymptotic value      250
Austin, D.      395
Average      30 158
Axiom of Choice      392
Baire’s theorem      97
Ball      9
Banach algebra      149 192 351
Banach space      95 331
Banach — inhaus theorem      98 101 356
Banach, S.      105
Bessel’s inequality      84 246
Beurling, A.      328 398 405
Beurling’s theorem      342
Bieberbach conjecture      397
Blaschke product      302 308 311 331 35C
Borel function      13 147 150
Borel measure      47
Borel set      12
Borel transform      399
Borel, E.      5 399
Boundary      109 204 240
Bounded function      16 64
Bounded linear functional      96 127 131
Bounded linear transformation      96
Bounded variation      118 161
box      49
Calderon, A. P.      397 398
Cancellation law      19
Canonical product      294 397
Cantor set      168
Cantor, D. G.      397
Caratheodory, C      393 396 397
Carleson, L.      399
Carrier      57
Cartesian product      7 136
Category theorem      98
Cauchy formula      208 235 254 266 333 335 380 384
Cauchy sequence      66
Cauchy theorem      206 259 299 369 372
Cauchy — Riemann equations      223 249
Cauchy, A.      396
Cauchy’s estimates      213
cell      49
Chain      316 391
Chain rule      199
Change of variables      174
CHARACTER      180
Characteristic function      11
Choice function      392
class      6
Closed curve      202
Closed graph theorem      116
Closed path      202
Closed set      12 35
Closed subspace      78
Closure      35
Cohen, P. J.      398 399
Collection      6
Commutative algebra      351
Commutative law      19 33
Compact set      35
Complement      7
Complete measure      27
Complete metric space      66 76 95
Completion of measure space      27 144
Completion of metric space      68 74
Complex algebra      351
Complex field      218 354
Complex homomorphism      193 360
Complex measure      16 131
Complex vector space      33
Complex-linear functional      105
Component      198
Composite function      7
Concentrated      121
Conformal equivalence      273
Conjugate exponents      62
Conjugate function      345
Connected set      198
Continuity      8 9
Continuous function      8
Continuous linear functional      80 96
Continuous measure      149
Continuum Hypothesis      143
Contour integral      219
Convergence in $L^p$      66
Convergence in measure      73
Convergence, almost uniform      214
Convergence, dominated      26
Convergence, monotone      21
Convergence, uniform      16
Convergence, uniform, on compact subsets      214
Convergence, weak      233 238
Convex function      60
Convex sequence      373
Convex set      78
Convexity theorem      244
Convolution      146 148 192
Coset      52 358
Cosine      2 251
Countable additivity      5 16 117
Counting measure      17
Cover      35 316
Covering theorem      154
Curve      202
Curve with orthogonal increments      94
Daniell, P. J.      394
Denjoy — Carleman theorem      376
Denjoy, A.      167
Dense set      56
density      177
Derivative      151 199
Derivative of Fourier transform      181
Derivative of function of bounded variation      166
Derivative of integral      165
Derivative of measure      153 155 173
Derivative of transformation      170
Derivative, lower      153
Derivative, symmetric      175
Derivative, upper      153
Determinant      174
Diagonal process      233 273
Diameter      152
Dieudonne, J.      394
Differentiable transformation      170 353
Differential      170 353
Dirchlet problem      228
Direct continuation      316
Discrete measure      149
Dise      9 198
Disjoint sets      7
Distance function      9
Distributive law      19 33 192
Division algebra      355
Domain      7
Dominated Convergence Theorem      26 28 181
Double integral      141
Dual space      108 128 238
Eberlein, W. F.      56
Edwards, R E.      394
Egoroff’s theorem      72
Elementary factor      293
Elementary set      136
ellipse      278
Ellis, H. W.      394
Empty set      6
End point      202
Entire function      199 301 370 397
Equicontmuous family      272
Equivalence classes      65
Equivalent paths      202
Essential range      73 364
Essential singularity      211 342
Essential supremum      64
Euclidean norm      169
Euclidean space      34 49
Euclid’s inequality      75
Euler’s identity      2
Exponential function      1 199
Exponential type      368 378 399
Extended real line      9
Extension      105
Extension theorem      105 385
Extremal function      242 348
Extreme point      238
Factorization      295 334 336
Family      6
Fatou, P.      396
Fatou’s Lemma      22 67 301 338
Fatou’s theorem      235
Fejer’s theorem      91
Field      358
Finite additivity      17
First category      98
Fixed point      220 285 308
Ford, L. R.      397
Fourier coefficients      81 91
Fourier coefficients of measure      134
Fourier series      91 267
Fourier transform      180 196 367
Fubini’s Theorem      140 144 395
Function      7
Function element      316
Function of bounded variation      161
Function of exponential type      368 399
Function, absolutely continuous      165
Function, analytic      199
Function, Borel      13
Function, bounded      64
Function, continuous      8
Function, convex      60
Function, entire      199
Function, essentially bounded      64
Function, exponential      1
Function, harmonic      223
Function, holomorphic      199
Function, Lebesgue integrable      24
Function, left-continuous      161 179
Function, locally integrable      196 237
Function, lower semicontinuous      37
Function, measurable      8 28 150
Function, meromorphic      260 296
Function, modular      320
Function, monotone      176
Function, normalized      81 161
Function, nowhere differentiable      115
Function, rational      219. 253 284
Function, simple      15 67
Function, singular      168
Function, subharmonic      328
Function, summable      24
Function, upper semicontinuous      37
Functional analysis      108
Functional, bounded      96
Functional, bounded on $C_0$      131
Functional, bounded on $L^p$      128
Functional, bounded on Hilbert space      80
Functional, bounded, complex-linear      105
Functional, bounded, continuous      96
Functional, bounded, linear      33
Functional, bounded, multiplicative      193 360
Functional, bounded, positive      34
Functional, bounded, real-linear      105
Fundamental theorem of calculus      165
Gap series      265 314 349 381 398
Gelfand transform      365
Gelfand — Mazur theorem      354
Gelfand, I.      398
Geometric mean      62
Goursat, E.      396
Graph      116 148
Greatest lower bound      7
Green’s Theorem      385
Hadamard, J.      250 314
Hahn decomposition      127
Hahn — Banach theorem      105 109 256 305 354 356 362
Halmos, P. R.      394 399
Hardy, G. H.      328
Harmonic conjugate      285 345
Harmonic function      223
Harmonic majorant      348
Harnack’s theorem      229
Hausdorff maximality theorem      87 107 177 357 392
Hausdorff separation axiom      36
Hausdorff space      36
Hausdorff — Young theorem      247
Hausdorff, F.      12 396 399
Heine — Borel theorem      36
Helson, H.      343 398
Herglotz, G.      396
Hilbert cube      93
Hilbert space      76 332
Hilbert space, isomorphism      86 92 187 341
Hoffman, K.      399
Holder’s Inequality      62 65
Holomorphic function      199
Homeomorphism      263
Homology      260
Homomorphism      181 193 357 365 399
Homotopy      260 319
Hurewicz, W.      395
Ideal      149 309 357 365
Image      7
Indefinite integral      157
Independent set      81
Index of curve      261
Index of path      204
Infimurn      7
Infinite product      290
Initial point      202
Inner factor      338
Inner function      336 342
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