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Hu S.-T. — Elements of real analysis
Hu S.-T. — Elements of real analysis

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Название: Elements of real analysis

Автор: Hu S.-T.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 378

Добавлена в каталог: 16.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      40
Absolute value      42
Absolutely closed      198
Absolutely continuous      303 343
Absolutely summable      232
Accumulation point      114
Addition      38
Additive function      275
Additive function, countably      276
Additive function, finitely      275
Adjoint      271
Adjoint operator      248
Adjoint space      240
Agree      11
Algebra      207
Algebra, Banach      215
Algebra, boolean      76
Algebra, normed      215
Algebra, pseudo-normed      214
Algebra, topological      212
Almost everywhere      84
Almost unique      304
Approximation      88 226
Archimedean ordered field      42
Arzela — Ascoli theorem      202
Associative      38
Automorphism      156
Automorphism, inner      156
Axiom of Choice      13 21
Axiom of countability      109 110
Axiom of countability, first      110
Axiom of countability, second      109
Baire category theorem      188
Baire measure      321
Ball      161 168
Ball, closed      161
Ball, open      168
Banach algebra      215
Banach fixed-point theorem      190
Banach space      214
Banach — Steinhaus theorem      259
Basic neighborhood      110
Basic open set      108
Basis      46 108 209
Basis, Hamel      46
Basis, local      110
Basis, neighborhood      110
Bernstein approximation theorem      226
Bernstein polynomials      226
Bessel inequality      266
Bidual space      245
Bijective      8
Bilinear      260
Binary operation      38
Bolzano — Weierstrass property      178
Boolean algebra      76
Boolean er-algebra      76
Borel set      80
Bound      21
Boundary      111
Boundary point      111
Bounded      56 67 173 175 204 216 239
Bounded convergence theorem      104 290
Bounded interval      47
Bounded linear operator      239
Bounded sequence      67
Bounded set      56 173
Bounded variation      337
Bounded, locally      216
Bounded, totally      175
Bounded, uniformly      204
Canonical imbedding      228 248
Canonical representation      91
Cantor's intersection theorem      191
Cardinality      24
Cartesian power      14
Cartesian product      13 17 144
Category      188
Cauchy sequence      185
Cauchy's criterion      236
Center      161
Characteristic function      11 88
Choice      13
Choice, axiom of      13
Circle group      152
class      19
Class, equivalence      19
Closed ball      168
Closed cover      122
Closed function      118
Closed graph theorem      257
Closed interval      47
Closed set      53 112
Closed unit interval      3
Closure      52 113
Cluster point      66 114 176
Coarser topology      108
Coefficient      264
Coefficient, Fourier      264
Combinable functions      11
Combination      209
Combination, linear      209
Combined function      11
Commutative      39
Compact      135
Compact, countably      176
Compact, Frechet      17S
Compact, locally      140
Compact, sequentially      177
Compactification      147
Compactification, maximal      151
Compactification, one-point      148
Compactification, Stone — Cech      150
Compactification, two-point      150
Complement      4
complete      21 185 279
Complete measure space      279
Complete ordered field      43
Complete orthogonal system      263
Completely normal      172
Completely regular      134
Completion      192 280
Complex measure      309
Component      143 300
Composable functions      8
Composed function      9
Composite      38
composition      9 23
Congruence mod p      19
Connected      141
Constant map      116
Contain      2
Contained in      2
continuous      58 62 116
Continuous linear operator      271
Continuous, almost everywhere      84
Continuous, uniformly      58 179
Continuously differentiable      347
Contraction      190
Converge      64 65 176 199 348
Converge, pointwise      69 199
Converge, uniformly      69 199
Converge, weakly      253
Convex      216
Convex hull      220
Convex, locally      216
Coordinate set      13
Coordinate space      127
Coset      155
Countability      28
Countability, first axiom of      110
Countability, second axiom of      109
Countable set      28
Countably additive      281
Countably compact      176
Counting measure      276
Cover      11 56 122
Cover, closed      122
Cover, open      122
Cover, Vitali      338
Cross-section      23 313
Daniell approach      314
Daniell integral      315
Daniell integral, lower      316
Daniell integral, regular      319
Daniell integral, upper      316
De Morgan's formulae      4
Decomposition      129
Decomposition space      141
Decomposition, Hahn      300
Decomposition, Jordan      302
Decomposition, Lebesgue      309
Decreasing      23
Delta function      247 350
Dense      57 114
Dense, nowhere      188
Derivative      332 336 350
Derivative, left      336
Derivative, Radon — Nikodym      307
Derivative, right      336
Derivative, total      334
Derived function      344
Derived set      114
Diagonal      14 128
Diagonal imbedding      128
Diagonal injection      14
Diameter      173
Difference      3
Difference, set-theoretic      3
Differentiable      332
Differentiable, continuously      347
Differentiable, infinitely      348
Dilation      220
Dini derivates      335
Dini's theorem      205
Dirac's delta function      247 350
Disconnected      141
Discrete group      152
Discrete metric      159 164
Discrete space      107
Discrete topology      108
Disjoint      4 124
Distance      48 161
Distance function      48 158
Distance function, usual      48
distribution      347
Distributive      40
diverge      65 176
Domain      6 36
Dominated Convergence Theorem      105 294
Dual operator      248
Dual space      240
Egoroff's theorem      90
Element      1
Element, least      21
Element, maximal      21
Element, minimal      21
Element, neutral      39
Empty      2
Endpoint      24
equal      3
Equal, almost everywhere      84
Equicontinuous functions      198
Equicontinuous functions, uniformly      204
Equipotent      24
Equivalence class      19
Equivalence relation      18
Equivalent      19
Equivalent pseudo-norms      220
Equivalent topology      118
Essential supremum      236
Euclidean norm      215
Euclidean space      127 164 207
Evaluation      18
Extended real line      150
Extended real numbers      46
Extension      10 121 284
Extension problem      121 146
Extension, linear      248
Extension, trivial      104 289
Exterior      111
Exterior point      111
Fatou's lemma      105 292
Field      40
Field, Archimedean ordered      43
Finer topology      108
Finite character      23
Finite intersection property      136
Finite measure      279
Finite set      33
First axiom of countability      110
First category      188
Fixed point      144 190
Fourier coefficient      264
Fourier series      265 268
Frechet compact      178
Frechet separation axiom      133
Frechet space      133
Frontier      111
Frontier point      111
Fubini's theorem      312
Function      6 36
Function of functions      9
Function, absolutely continuous      243
Function, bijective      8
Function, characteristic      11 88
Function, closed      118
Function, combined      11
Function, composed      9
Function, constant      7
Function, continuous      58 116
Function, derived      344
Function, Dirac's delta      350
Function, distance      48 161
Function, generalized      350
Function, identity      8
Function, inclusion      8
Function, induced      23
Function, injective      7
Function, integrable      288 317
Function, interior      118
Function, inverse      8
Function, isometric      181
Function, linear      8 237
Function, lower semicontinuous      179
Function, measurable      83 286 319
Function, open      118
Function, real-valued      57
Function, set      275
Function, simple      88 286
Function, step      88
Function, sublinear      248
Function, submetric      181
Function, summable      274
Function, surjective      7
Function, uniformly continuous      58
Function, upper semicontinuous      179
Functional      237
Functional analysis      254
Functional, linear      237
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