Hewitt E., Stromberg K. — Real and abstract analysis: a modern treatment of the theory of functions of a real variable :: Электронная библиотека попечительского совета мехмата МГУ

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Hewitt E., Stromberg K. — Real and abstract analysis: a modern treatment of the theory of functions of a real variable

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Название: Real and abstract analysis: a modern treatment of the theory of functions of a real variable

Авторы: Hewitt E., Stromberg K.

Аннотация:

Hewitt E., Stromberg K. Real and abstract analysis (Springer, 1965, 1975 printing)(ISBN 0387901388)

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 486

Добавлена в каталог: 07.02.2014

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Предметный указатель

Suhomlinov      213
Summability of Fourier integrals      404
Summability of Fourier series, Abel      301
Summability of Fourier series, Ces $\grave{a}$ ro      293
Summability of Fourier series, uniform      300
Summable function      173
Sums, Darboux      106
Sums, Lebesgue      183
Suppes, P.      1
Support of a measure      122
Supremum in       69
Supremum in an ordered field      44
Supremum, essential      346
Symmetric derivative of a function      271
Symmetric difference of two sets      4
Tarski, A.      22
Term by term differentiation      267
Term by term integration      171 175
Term of a sequence      10
Ternary set, Cantor      13 70
Theorem, Alexander’s subbase      64
Theorem, B. Levi’s      172
Theorem, Baire category      68 79
Theorem, Banach — Steinhaus      218
Theorem, Banach’s Fixed-Point      78
Theorem, Cantor — Bendixson      72
Theorem, closed graph      217
Theorem, Dini’s      205
Theorem, Egorov’s      158
Theorem, Fej $\acute{e}$ r — Lebesgue      294
Theorem, Fubini’s      384 386
Theorem, generalized B. Levi      118
Theorem, Hahn decomposition      306
Theorem, Hahn — Banach      212
Theorem, Hardy — Littlewood maximal      424 425 426
Theorem, Heine — Borel      66
Theorem, Hopf’s extension      142
Theorem, Jordan decomposition      266
Theorem, K $\ddot{o}$ nig’s      27
Theorem, Krein’s extension      220
Theorem, Lebesgue — Radon — Nikod $\acute{y}$ m      315 318 323
Theorem, Lebesgue’s decomposition      326
Theorem, Lebesgue’s differentiation      264
Theorem, Lebesgue’s dominated convergence      172 174 185
Theorem, Luzin’s      159
Theorem, monotone convergence      172
Theorem, open mapping      215
Theorem, Plancherel’s      411
Theorem, Radon — Riesz      233
Theorem, Riesz representation      177 364
Theorem, Riesz — Fischer      250
Theorem, Schr $\ddot{o}$ der — Bernstein      20
Theorem, Steinhaus      143
Theorem, Stone — Weierstrass      94 95 97 98
Theorem, Tietze’s Extension      99
Theorem, Tihonov’s      65
Theorem, Vitali’s convergence      203
Theorem, Vitali’s covering      262
Theorem, Weierstrass approximation      96
Theorem, well-ordering      14
Tietze’s extension theorem      99
Tihonov, A.      65
Tihonov’s theorem      65
Topological space      55
Topological space, dense subset of a      61
Topological space, density character of a      219
Topological space, subspace of a      60
Topological spaces, Cartesian product of      65
topology      55
Topology for , usual      56
Topology for $R^{n}$ or $K^{n}$ , usual      60
Topology for R, usual      56
Topology, base for a      58
Topology, discrete      56
Topology, indiscrete      56

Topology, metric      60
Topology, order      79
Topology, product      65
Topology, relative      60
Topology, subbase for a      58
Total variation norm      271
Total variation of a complex measure      308
Total variation of a complex measure function      266 270 272
Total variation of a complex measure, signed measure      307
Transfinite induction      17
Transform, Fourier      249 401
Transform, Plancherel      411
Transformation      9
Transformation, bounded linear      210
Transformation, linear      210
Translate of a function      110
Translation in $\mathfrak{L}_{p}$ , continuity of      199
Trigonometric polynomials      248
Tukey’s lemma      14
Ultimately equal sequences      443
Ultrafilter      358
Unbounded interval      54
Uncountable set      22
Uniform boundedness principle      217
Uniform norm      83
Uniform spaces      87
Uniform summability of Fourier series      300
Uniformly continuous function      87
Uniformly convex Banach spaces      232
Uniformly integrable sequences of functions      204
Uniformly rotund Banach spaces      232
Unions of sets      2
Uniqueness of Lebesgue measure      185
Uniqueness theorem for Fourier transforms      408
Unit of a ring      33
Unit point mass      120
Unit, approximate      400
Unitary -space      13
Upper bound      13
Upper semicontinuous function      88
Urysohn, P.      75
Urysohn’s lemma      75
Usual topology for       56
Usual topology for       56
Usual topology for $R^{n}$ or $K^{n}$       60
Value of a function      9
Variation      see Total variation
Variation of a signed measure, negative      307
Variation of a signed measure, positive      307
Variation of a signed measure, total      307
Vector space      17 31
Vector space, algebraic dimension of a      31
Vector space, basis for a      18
Vector space, linear dimension of a      31
Vitali cover      262
Vitali’s convergence theorem      203
Vitali’s covering theorem      262
Void set      2
Weak convergence      233
Weak convergence in $\mathfrak{L}_{p}$       206
Weak law of large numbers      452
Weierstrass approximation theorem      96
Weierstrass, K.      66 90 258
Well-ordered set      8
Well-ordered set, initial segment of a      16
Well-ordering theorem      14
Young, W. H.      414
Young’s inequality      189
Zaanen, A. C.      203
Zermelo, E.      12 14
Zero-one law      443
Zero-one measures      358
Zorn’s Lemma      14
Zuckerman, H. S.      458
Zygmund, A.      203 292 298

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