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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/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 1986

Количество страниц: 416

Добавлена в каталог: 14.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathrm{F}_\sigma$-set      12
$\mathrm{G}_\delta$-set      12
$\pi$      3
$\sigma$-algebra      8
$\sigma$-compact set      47 7
$\sigma$-finite measure      47 7
$\sigma$-ring      397
Absolute continuity      120
Absolute continuity of functions      145
Absolute convergence      116
Absolutely convergent Fourier series      367
Addition formula      1
Affine transformation      377
Ahlfors, L.V.      402
Algebra      356
Algebra of measures      175
Algebra of sets      10
Algebraically closed field      213
Almost everywhere      27
Almost periodic function      94
Almost uniform convergence      214
Analytic continuation      323 377 379
Analytic function      197
Annulus      229 264 292
Approach region      240
Area      250
Area theorem      286
Arens, R.      398
Argument      204
Arithmetic mean      63
Arzela — Ascoli theorem      245
Associative law      18
Asymptotic value      265
Austin, D.      399
Average      30
Axiom of Choice      396
Baire's theorem      97
Balanced collection      268
Ball      9
Banach algebra      190 356
Banach space      95
Banach — Steinhaus theorem      98
Banach, S.      105
Bessel's inequality      85 260
Beurling's theorem      348
Beurling, A.      335 402
Bieberbach conjecture      401
Blaschke product      310 317 318 338 353
Bledsoe, W.W.      399
Borel function      12
Borel measure      47
Borel set      12
Borel transform      402
Borel, E.      5 402
Boundary      108 202 289
Bounded function      66
Bounded linear functional      96 113 127 130
Bounded linear transformation      96
Bounded variation      117 148 157
box      50
Brouwer's fixed point theorem      151
Calderon, A.P.      401 402
Cancellation law      19
Canonical product      302
Cantor set      58 145
Cantor, D.G.      401
Caratheodory, C      397 400 401
Carleson, L.      398
Carrier      58
Cartesian product      7 160
Category theorem      98
Cater, F.S.      398
Cauchy formula      207 219 229 268 341 384 388
Cauchy sequence      67
Cauchy theorem      205 206 207 218
Cauchy — Riemann equations      232
Cauchy's estimates      213
Cauchy, A.      400
cell      50
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
Completion of metric space      70 74
Complex algebra      356
Complex field      213 359
Complex homomorphism      191 362
Complex measure      16 116
Complex vector space      33
Complex-linear functional      105
Component      197
Composite function      7
Concentrated      119
Conformal equivalence      282
Conjugate exponents      63
Conjugate function      350
Connected set      196
Continuity      8 9
Continuous function      8
Continuous linear functional      81 96 113 127 130
Continuous measure      175
Continuum Hypothesis      167
Convergence in $\mathrm{L}^p$      67
Convergence in measure      74
Convergence, almost uniform      214
Convergence, dominated      26
Convergence, monotone      21
Convergence, uniform on compact subsets      214
Convergence, 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
Curve with orthogonal increments      94
CYCLE      218
Daniell, P.J.      398
de Branges, L.      401
Denjoy — Carleman theorem      380
Denjoy, A.      144
Dense set      58
Derivative      135 197
Derivative of Fourier transform      179
Derivative of function of bounded variation      1
Derivative of integral      141
Derivative of measure      136 142 143 241
Derivative of transformation      150
Derivative, symmetric      136
Determinant      54
Diagonal process      246
Dieudonne, J.      398
Differentiable transformation      150
Differential      150
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      26 180
Double integral      165
Dual space      108 112 127 130
Eberlein, W.F.      58
Edwards, R.E.      398
EgorofTs theorem      73
Elementary factor      301
Elementary set      161
ellipse      287
Ellis, H.W.      399
Empty set      6
End point      200
Entire function      198
Equicontinuous family      245
Equivalence classes      67
Equivalent paths      201
Essential range      74
Essential singularity      211 267
Essential supremum      66
Euclid's inequality      77
Euclidean space      34 49
Euler's identity      2
Exponential function      1 198
Exponential type      372 382 383
Extended real line      7 9
Extension      105
Extensiop theorem      105
Extremal function      255
Extreme point      251
Factorization      303 338 344
Family      6
Fatou's lemma      23 68 309 344
Fatou's theorem      249
Fatou, P.      400
Fejer kernel      252
Fejer's theorem      91
Field      394
Finite additivity      17
First category      98
Fixed point      151 229 247 293 297 314 318
Ford, L.R.      401
Fourier coefficients      82 91
Fourier coefficients of measure      133
Fourier series      83 91
Fourier transform      178
Fubini's theorem      164 168
Function      7
Function element      323
Function of bounded variation      148
Function of exponential type      372 383
Function, absolutely continuous      145
Function, analytic      197
Function, Borel      13
Function, bounded      66
Function, complex      8
Function, continuous      8
Function, convex      61
Function, entire      198
Function, essentially bounded      66
Function, exponential      1
Function, harmonic      232
Function, holomorphic      197
Function, Lebesgue integrable      24
Function, left-continuous      157
Function, locally integrable      194
Function, lower semicontinuous      37
Function, measurable      8 29
Function, meromorphic      224
Function, modular      328
Function, nowhere differentiable      114
Function, rational      267
Function, real      8
Function, simple      15
Function, subharmonic      335
Function, summable      24
Function, upper semicontinuous      37
Functional analysis      108
Functional on $\mathrm{C}_0$      130
Functional on $\mathrm{L}^p$      127
Functional on Hilbert space      81
Functional, bounded      96
Functional, complex-linear      105
Functional, continuous      96
Functional, linear      33
Functional, multiplicative      191 364
Functional, positive      34
Functional, real-linear      105
Fundamental domain      329
Fundamental theorem of calculus      144 148
Gap series      276 321 334 354 385
Gelfand transform      370
Gelfand — Mazur theorem      359
Gelfand, L      402
Geometric mean      63
Goursat, E.      400
Graph      114 174
Greatest lower bound      7
Green's theorem      389
Hadamard,J.      264 321
Hahn — Banach theorem      104 107 270 313 359
Hahn, decomposition      126
Hall, D.      398
Halmos, P.R.      398 403
Hardy's inequality      72 177
Hardy, G.H.      173 335 399
Harmonic conjugate      350
Harmonic function      232
Harmonic majorant      352
Harnack's theorem      236 250
Hausdorff maximality theorem      87 107 195 362 396
Hausdorff separation axiom      36
Hausdorff space      36
Hausdorff — Young theorem      261
Hausdorff, F.      12 400
Heine — Borel theorem      36
Helson, H.      348
Herglotz, G.      400
Hilbert cube      92
Hilbert space      77
Hilbert space isomorphism      86
Hoffman, K.      402
Holder's inequality      63 66
Holomorphic function      197
Homomorphism      179 191 364 402
Homotopy      222
Hunt, R.A.      398
Ideal      175 305 362
Image      7
Independent set      82
Index of curve      223 230
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