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

Diameter of a set      67
Differentiability of monotone functions      264
Differentiable function      257
Differentiation on a net      373
Differentiation theorem, Lebesgue’s      264
Differentiation, term by term      267
Dimension of $\mathfrak{L}_{2}$ , orthogonal      255
Dimension of a Hilbert space, orthogonal      247
Dimension of a vector space, algebraic      31
Dimension of a vector space, linear      31
Dimension, Hausdorff      145
Dini derivates      257
Dini’s theorem      205
Dirac measure      120
Dirichlet kernel      292
Discontinuities of a function, set of      78
Discontinuous measures, purely      334
Discrete metric      59
Discrete topology      56
Disjoint sets      3
Dissection, measurable      164
Distance between two sets      78
Distance from a point to a set      77
Distance function      59
Divergent Fourier series      300
Domain of a relation      7
Dominated convergence theorem, Lebesgue’s      172 174 185
Doob, J. L.      373
Dual space      211
Dunford, N.      210
Egorov’s theorem      158
Endpoints      54
Enumeration of a set      22
Equivalence relation      8
Equivalent sets      19
Essential supremum      346
Essentially bounded functions      346
Euclidean metric      59
Euclidean n-space      13
Evaluation functional      114
EXP      51
Expansions of real numbers      46 47
Exponential function      51
Extended real numbers      54
Extending a measure      162
Extension of a relation      8
Extension of Lebesgue measure, invariant      359
Extension of the Riemann integral, Lebesgue integral as an      184
Extension theorem, Hahn — Banach      212
Extension theorem, Hopf’s      142
Extension theorem, Kre $\breve{\imath}$ n’s      220
Extension theorem, Tietze’s      99
Extensions of Lebesgue measure      137 359
Extensions of measures      141 148
Family of finite character      13
Family, monotone      380
Fatou’s Lemma      124 172
Fej $\acute{e}$ r — Lebesgue theorem      294
Fej $\acute{e}$ r, L.      292
Fej $\acute{e}$ r’s kernel      292 408
Field      34
Field of complex numbers      48
Field, Archimedean ordered      37
Field, automorphisms of the real      48
Field, characteristic of a      34
Field, complete Archimedean ordered      44
Field, completion of an ordered      38
Field, non — Archimedean ordered      46
Field, ordered      35
Field, real number      46
Filter      358
Filter, fixed      358
Filter, free      358
Finite character, family of      13
Finite intersection property      62
Finite measure space      127
Finite set      21
Finite variation, function of      266
Finitely additive measures      126 354
Finitely additive measures, integral for      355
Finitely additive measures, regular      364
Finitely additive signed measure, Jordan decomposition of      338
Finjte measure      127
First category      68
First mean value theorem for integrals      420
Fixed filter      358
Fixed-point theorem, Banach’s      78
Flett, T. M.      428
Fourier coefficients      237 249
Fourier integrals, summability of      404
Fourier series      245 291
Fourier series, Abel summability of      301
Fourier series, arithmetic means for a      292
Fourier series, Ces $\grave{a}$ ro summability for      293
Fourier series, divergent      300
Fourier series, uniform summability of      300
Fourier transform      249 401
Fourier transform on $\mathfrak{L}_{2}$       411
Fourier transform, inversion of      409
Fourier transform, uniqueness theorem for the      408
Fr $\acute{e}$ chet compact space      62
Free filter      358
Fubini, G.      267
Fubini’s Theorem      384 386
Function      9
Function of bounded variation      266
Function of finite variation      266
Function, absolutely continuous      282
Function, additive on       49
Function, Baire      163
Function, Banach indicatrix of a      271
Function, Borel measurable      149 187
Function, bounded      83
Function, choice      12
Function, constant      82
Function, continuous      73
Function, continuous, that vanishes at infinity      86
Function, continuous, that vanishes in a neighborhood of infinity      86
Function, continuous, with compact support      86
Function, convex      202 271
Function, differentiable      257
Function, distance      59
Function, exponential      51
Function, indefinite integral of a      272
Function, integrable      173
Function, Lebesgue measurable      149
Function, Lebesgue points for a      278
Function, Lebesgue set for a      278
Function, Lebesgue’s singular      113
Function, locally integrable      186
Function, locally null      123
Function, lower semicontinuous      88
Function, measurable      149 154
Function, monotone      105
Function, nondecreasing      105
Function, nonincreasing      105
Function, normalized nondecreasing      112 330
Function, null      123
Function, onto      10
Function, oscillation      78
Function, reflection of a      110
Function, Riemann — Stieltjes integrable      106
Function, section of a      379
Function, set of discontinuities of a      78
Function, simple      159
Function, step      198
Function, strictly decreasing      105
Function, strictly increasing      105
Function, summable      173
Function, symmetric derivatives of a      271

Function, total variation of      266 270 272
Function, translate of a      110
Function, uniformly continuous      87
Function, upper semicontinuous      88
Function, value of a      9
Functional, evaluation      114
Functional, linear      211
Functional, multiplicative linear      114 365
Functional, nonnegative linear      114 220
Functional, sublinear      212
Functionals on $\mathfrak{L}_{1}(R)$ , multiplicative linear      417
Functionals on Hilbert spaces, bounded linear      248 255
Functions,       288 303
Functions, convolution of      396
Functions, differentiability of monotone      264
Functions, Hermite      243
Functions, integral representation of convex      300
Functions, lattice of      82
Functions, normalized Hermite      245
Functions, pointwise limits of continuous      79
Functions, separating family of      93
Functions, singular      278
Functions, uniformly integrable sequences of      204
Fundamental theorem of the integral calculus for Lebesgue integrals      285
Gauss’s kernel      408
Generalization of monotone convergence theorem      118
Generalized B. Levi theorem      118
Generalized H $\ddot{o}$ lder’s inequality      200
Generated by a family, $\sigma$ -algebra      132
Geometric interpretation of the complex field      50
Gram — Schmidt orthonormalization process      240
Greatest lower bound in an ordered field      44
Group      32
Group algebra of       399
H $\ddot{o}$ lder’s inequality for $0< p <\infty$       191
H $\ddot{o}$ lder’s inequality for $1< p <\infty$       190
H $\ddot{o}$ lder’s inequality, generalized      200
Hahn decomposition      305
Hahn decomposition theorem      306
Hahn — Banach theorem      212
Half-open intervals      54
Halmos, P.      1
Hamel basis      18
Hamilton, Sir W. R.      102
Hardy — Littlewood maximal theorem      424 425 426
Hardy, G. H.      258 422
Hausdorff dimension      145
Hausdorff maximality principle      14
Hausdorff measure      145
Hausdorff space      56
Heine — Borel theorem      66
Heine — Borel — Bolzano — Weierstrass theorem      66
Hermite functions      243
Hermite functions, completeness of the      416
Hermite functions, normalized      245
Hermite polynomials      243
Hewitt, E.      137 250 378 445
Hewitt, M.      32
Hilbert parallelotope      254
Hilbert space      196 235
Hilbert space, bounded linear functionals on a      248 255
Hilbert space, orthogonal dimension of a      247
Hilbert space, pre      195
Hilbert space, projections in a      253
Hirschman Jr., I. I.      250
Holladay, J. C.      103
Hopf’s extension theorem      142
Huntington, E. V.      5
Ideals in $\mathfrak{C}_{0}(X)$       365
Ideals in $\mathfrak{L}_{1}(R)$       417
Ideals in a ring      33
Identity, Parseval’s      245 246 250
Identity, polar      235
Image sets, measures on      161
Images of measures, continuous      180
Imaginary part of a complex number      48
Increasing function, strictly      105
Indefinite integral of a function      272
Indefinite integral, derivative of an      275
Independence, linear      17
Indicatrix of a function, Banach      271
Indiscrete topology      56
Induction, transfinite      17
Inequalities, Clarkson’s      225 227
Inequalities, H $\ddot{o}$ lder’s      190 191
Inequalities, Jensen’s      202
Inequality, Bessel’s      239
Inequality, Bunyakovski $\breve{\imath}$ ’s      190
Inequality, Cauchy — Bunyakovski $\breve{\imath}$ — Schwarz      234
Inequality, Cauchy’s      190
Inequality, generalized H $\ddot{o}$ lder’s      200
Inequality, Minkowski’s      191
Inequality, Schwarz’s      190 234
Inequality, Young’s      189
Infimum in       69
Infimum in an ordered field      44
Infinite product measures      432
Infinite product measures, absolute continuity of      453
Infinite product measures, singular measures induced by      456
Infinite product measures, singularity of      453
Infinite product spaces, iterated integrals on      439
Infinite products of measure spaces      429
Infinite set      21
Infinite set, countably      22
Initial segment      28
Initial segment of a well ordered set      16
Inner product space      195 234
Integers      2
Integers, positive      2
Integrability, Riemann      105 183
Integrable function      173
Integrable function, locally      186
Integrable function, Riemann — Stieltjes      106
Integral as a set function      175
Integral of a function, indefinite      272
Integral relative to a complex measure      312
Integral representation of convex functions      300
Integral, absolute continuity of the      176
Integral, Denjoy      299
Integral, derivative of an indefinite      275
Integral, iterated      385
Integral, Lebesgue      164
Integral, Lebesgue integral as an extension of the Riemann      184
Integral, linearity of the      169 171 174
Integral, Riemann      107
Integral, Riemann — Stieltjes      106
Integrals as areas      392
Integrals for finitely additive measures      355
Integrals on infinite product spaces, iterated      439
Integrals on the completion of a measure space      186
Integrals, change of variable in      342
Integrals, first mean value theorem for      420
Integrals, fundamental theorem of the integral calculus for Lebesgue      285
Integrals, integration by parts for Lebesgue — Stieltjes      419
Integrals, second mean value theorem for      420
Integrals, summability of Fourier      404
Integration by parts      287
Integration by parts for Lebesgue — Stieltjes integrals      419
Integration by substitution      342
Integration, term by term      171 175
Interior of a set      56
Intersections of sets      2
Interval, bounded      54
Interval, closed      54
Interval, open      54
Interval, subdivision of an      105
Interval, unbounded      54
Intervals, component      69
Intervals, Half-open      54
Invariant extension of Lebesgue measure      359

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