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Folland J.B. — Real Analysis: Modern Techniques and Their Applications
Folland J.B. — Real Analysis: Modern Techniques and Their Applications



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Название: Real Analysis: Modern Techniques and Their Applications

Автор: Folland J.B.

Аннотация:

This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1999

Количество страниц: 386

Добавлена в каталог: 09.12.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Subsequence      4
Subspace of a vector space      151
Support of a distribution      284
Support of a function      132
Support of a measure      215
Supremum      9—10
Surjective mapping      4
Symbol      273
Symbol, principal      306
Symmetric difference      3
Symmetric neighborhood      339
Tagged partition      82
Tempered distribution      293
Tempered function      293
Theorem, Alaoglu's      169
Theorem, Arzela — Ascoli      137
Theorem, Baire category      161
Theorem, Caratheodory's      29
Theorem, central limit      326
Theorem, closed graph      163
Theorem, dominated convergence      54
Theorem, Egoroff's      62
Theorem, Fourier inversion      251
Theorem, Fubini — Tonelli      67—68 229
Theorem, Hahn decomposition      86
Theorem, Hahn — Banach      157—158
Theorem, Jordan decomposition      87
Theorem, Krein extension      161
Theorem, Lebesgue differentiation      98
Theorem, Lebesgue — Radon — Nikodym      90 93
Theorem, Liouville's      300
Theorem, Lusin's      64 217
Theorem, Marcinkiewicz interpolation      202
Theorem, maximal      96
Theorem, moment convergence      320
Theorem, monotone convergence      50
Theorem, open mapping      162
Theorem, Plancherel      252
Theorem, Pythagorean      173
Theorem, Radon — Nikodym      91
Theorem, Rellich's      305
Theorem, Riesz representation      212 223
Theorem, Riesz — Thorin interpolation      200
Theorem, sampling      255
Theorem, Schroeder — Bernstein      7
Theorem, Shannon's      324
Theorem, Sobolev embedding      303 308
Theorem, Stone — Weierstrass      139 141
Theorem, Tietze extension      122 131
Theorem, Tychonoff's      136
Theorem, Urysohn metrization      145
Theorem, Vitali convergence      187
Theorem, Vitali covering      110
Theorem, Weierstrass approximation      141 318
Three lines lemma      200
Tietze extension theorem      122 131
Tonelli's theorem      67—68 229
Topological group      339
Topological space      113
Topological vector space      165
topology      113
Topology of uniform convergence      133
Topology of uniform convergence on compact sets      133
Topology, cofinite      113
Topology, generated by a family of sets      114
Topology, indiscrete      113
Topology, norm      152
Topology, product      120
Topology, quotient      124
Topology, relative      114
Topology, strong operator      169
Topology, trivial      113
Topology, vague      223
Topology, weak      120 168
Topology, weak operator      169
Topology, weak*      169
Topology, Zariski      117
Torus      238
Total ordering      5
Total variation of a complex measure      93
Total variation of a function      102
Total variation of a signed measure      87
Totally bounded set      15
Transfinite induction      9
TRANSPOSE      160
Triangle inequality      151
Trivial topology      113
Tychonoff space      123
Tychonoff's theorem      136
U rysohn metrization theorem      145
Uniform boundedness principle      163
Uniform continuity      238 340
Uniform integrability      92
Uniform norm      121
Unimodular group      346
Unitary map      176
Upper bound      5
Upper semi continuous function      218
Urysohn's lemma      122 131 245
USC function      218
Vague topology      223
Vanish at infinity      132
Variance      314—315
Vitali convergence theorem      187
Vitali covering theorem      110
Wave equation      275
Weak $L^P$      198
Weak convergence      169
Weak law of large numbers      321
Weak operator topology      169
Weak topology      120 168
Weak type      202
Weak* topology      169
Weaker topology      114
Weierstrass approximation theorem      141 318
Weierstrass kernel      260
Well ordering      5
Well Ordering Principle      5
Weyl's lemma      308
Wiener process      332
Wiener process, abstract      331
Wirtinger's inequality      254
Young's inequality      240—241
Zariski topology      117
Zorn's lemma      5
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