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

$F_{\sigma}$ set      68
$G_{\delta}$ -set      68
-functions      288 303
-space, Euclidean      13
-space, unitary      13
, additive functions on      49
, characters of      301
, group algebra of      399
, open set in      55
, regular Borel measures on      329
, structure of open sets in      69
, usual topology for      56
$\check{C}$ ech, E.      65
$\mathfrak{B}^{r}(R)$ , invariant mean on      359
$\mathfrak{C}_{0}(X)$ , conjugate space of      364
$\mathfrak{C}_{0})X)$ , ideals in      365
$\mathfrak{L}_{1}$ spaces      173
$\mathfrak{L}_{1}$ , conjugate space of      353
$\mathfrak{L}_{1}(R)$ , ideals in      417
$\mathfrak{L}_{1}(R)$ , multiplicative linear functionals on      417
$\mathfrak{L}_{2}$ , Fourier transform on      411
$\mathfrak{L}_{2}$ , orthogonal dimension of      255
$\mathfrak{L}_{p}$ norm      188
$\mathfrak{L}_{p}$ spaces      173
$\mathfrak{L}_{p}$ , completeness of      192
$\mathfrak{L}_{p}$ , conjugate space of      230
$\mathfrak{L}_{p}$ , continuity of translation in      199
$\mathfrak{L}_{p}$ , dense subsets of      197
$\mathfrak{L}_{p}$ , weak convergence in      206
$\mathfrak{L}_{\infty}$ spaces      347
$\mathfrak{L}_{\infty}$ , conjugate space of      357
$\sigma$ -algebra      4
$\sigma$ -algebra generated by a family      132
$\sigma$ -algebra, product      379
$\sigma$ -compact set      138
$\sigma$ -compact set space      125
$\sigma$ -finite measure      127
$\sigma$ -finite measure space      127
$\sigma$ -finite set      138
$\sigma$ -ring      4
$\varepsilon$ -neighborhood      60
Abel summability of Fourier series      301
Abel, N. H.      32
Abelian group      32
Abel’s kernel      407
Absolute continuity of infinite product measures      453
Absolute continuity of the integral      176
Absolute value      48
Absolutely continuous functions      282
Absolutely continuous functions, composition of      297
Absolutely continuous measure      312
Absolutely continuous measure, derivative of an      328
Additive functions on       49
Adjoint of a linear operator      221 251
Adjoint space      211
Alexander’s subbase theorem      64
Algebra of , group      399
Algebra of operators      251
Algebra of sets      4
Algebra over a field      82
Algebra, Banach      84
Algebra, linear      82
Algebra, normed      83
Algebraic dimension of a vector space      31
Algebras, Boolean      5
Almost everywhere      122 155
Almost everywhere, locally      122
Almost uniform convergence      158
Analytic sets      133
Approximate unit      400
Approximation by simple functions      159
Approximation theorem, Weierstrass      96
Archimedean ordered field      37
Archimedean ordered field, complete      44
Archimedean ordered field, non      46
Areas, integrals as      392
arg      50
Arithmetic means for a Fourier series      292
Arithmetic, cardinal number      23
Automorphism      33
Automorphisms of the real field      48
Axiom of Choice      12
Baire category theorem      68 79
Baire functions      163
Baire functions of type $\alpha$       163
Baire sets      164
Ball, open      60
Banach algebra      84
Banach indicatrix of a function      271
Banach space      84
Banach space, conjugate of a      211
Banach space, locally uniformly convex      233
Banach space, products of      217 221
Banach space, quotient spaces of      221
Banach space, reflexive      215
Banach space, uniformly convex      232
Banach space, uniformly rotund      232
Banach — Steinhaus theorem      218
Banach, S.      80 137 215 261 263 288
Banach’s fixed-point theorem      78
Base for a topology      58
Basis for a vector space      18
Basis, Hamel      18
Basis, linear      18
Bernstein, F.      146
Bessel’s inequality      239
Binomial coefficients      90
Binomial series      90
Birkhoff, G.      5
Birnbaum — Orlicz spaces      203
Bohnenblust, H. F.      213
Bolzano      66
Bolzano — Weierstrass property      62
Boole, G.      5
Boolean algebra      5
Boolean ring      5
Borel measurable function      149 187
Borel measures      329
Borel measures on , regular      329
Borel measures, complex regular      360
Borel sets      132
Borel sets in product spaces      391
Borel — Cantelli lemma      445
Borel, E.      66
Bound in an ordered field, greatest lower      44
Bound in an ordered field, least upper      44
Bound, lower      13
Bound, upper      13
Boundary      56
Bounded functions      83
Bounded functions, essentially      346
Bounded interval      54
Bounded linear functionals on Hilbert spaces      248 255
Bounded linear transformation      210
Bounded sequence      38
Bounded set in a metric space      66
Bounded variation, function of      266
Bunyakovski $\breve{\imath}$ ’s inequality      190
Cantor ternary set      13 70
Cantor — Bendixson Theorem      72
Cantor, G.      21 67
Cantor-like set      70
Carath $\acute{e}$ odory, C.      126 127
Cardinal numbers      19
Cardinal numbers, arithmetic of      23
Cardinal numbers, no largest      21
Cardinal numbers, order relation for      20
Cardinality      19
Cartesian product of a family of sets      12
Cartesian product of topological spaces      65

Cartesian product of two sets      7
Category theorem, Baire      68 79
Category, first      68
Category, second      68
Cauchy sequence      38 67
Cauchy — Bunyakovski $\breve{\imath}$ — Schwarz inequality      234
Cauchy’s inequality      190
Ces $\grave{a}$ ro summability for Fourier series      293
Chain rule      328
Change of variable in integrals      342
Characteristic function of a set      11
Characteristic of a field      34
Characters of       301
Choice function      12
Choice, axiom of      12
Clarkson, J. A.      231
Clarkson’s inequality for $1 \leq p<2$       227
Clarkson’s inequality for $2 \leq p<\infty$       225
Closed graph theorem      217
Closed interval      54
Closure of a set      56
Coefficients, binomial      90
Coefficients, Fourier      237 249
Cohen, P. J.      12 30
Commutative ring      33
Compact space      62
Compact space, $\sigma-$       125
Compact space, Fr $\acute{e}$ chet      62
Compact space, locally      74
Compact space, sequentially      62
Compact support, continuous functions with      86
Complement of a set      4
Complement of a subspace, orthogonal      252
Complete Archimedean ordered field      44
Complete measure      155
Complete measure space      155
Complete metric space      67
Complete orthonormal set      240 242
Completeness of $\mathfrak{L}_{p}$       192
Completeness of the Hermite functions      416
Completeness of the trigonometric functions      248
Completion of a measure space      155
Completion of a measure space, integrals on      186
Completion of a metric space      77
Completion of a normed linear space      221
Completion of an ordered field      38
Complex conjugate      48
Complex field, geometric interpretation of the      50
Complex measure      304
Complex measure, integral relative to a      312
Complex measure, Jordan decomposition of a      309
Complex measure, total variation of a      308
Complex measures, Lebesgue — Radon — Nikod $\acute{y}$ m theorem for      323
Complex number field      48
Complex number, imaginary part of a      48
Complex number, real part of a      48
Complex plane      50
Component intervals      69
Composition of absolutely continuous functions      297
Composition of relations      8
Condition       288
Cone, convex      219
Conjugate of a Banach space      211
Conjugate space      211
Conjugate space of $\mathfrak{C}_{0}(X)$       364
Conjugate space of $\mathfrak{L}_{1}$       353
Conjugate space of $\mathfrak{L}_{p}$       230
Conjugate space of $\mathfrak{L}_{\infty}$       357
Conjugate space, second      211
Conjugate, complex      48
Connected space      57
Constant function      82
Content, Jordan      121
Continuity at a point      73
Continuity of translation in $\mathfrak{L}_{p}$       199
Continuous function      73
Continuous function, uniformly      87
Continuous functions that vanish at infinity      86
Continuous functions that vanish in a neighborhood of infinity      86
Continuous functions with compact support      86
Continuous functions, absolutely      282
Continuous functions, point wise limits of      79
Continuous functions, uniformly      87
Continuous images of measures      180
Continuous measures      334
Continuous nowhere differentiable functions      258
Continuous, left      111
Continuous, right      111
Continuum      19
Continuum Hypothesis      30
Contraction mapping      78
Convergence in measure      156
Convergence in measure, metric of      183
Convergence in probability      156
Convergence theorem, Lebesgue’s dominated      172 174 185
Convergence theorem, monotone      172
Convergence theorem, Vitali’s      203
Convergence weak, in $\mathfrak{L}_{p}$       206
Convergence, almost uniform      158
Convergence, weak      233
Convergent sequence      62
Convex cone      219
Convex functions      202 271
Convex functions, integral representation of      300
Convex set      252
Convolution of functions      396
Coordinate      12
Coordinate space, projection onto a      65
Countable set      22
Countably additive measure      126
Countably infinite set      22
Counting measure      127
Cover      62
Cover, open      62
Cover, Vitali      262
Covering theorem, Vitali’s      262
Cut in an ordered field, Dedekind      46
Daniell, P. J.      114
Darboux sums      106
de Morgan’s laws      4
Decomposable measures      317
Decomposable measures, Lebesgue decomposition for      341
Decomposable measures, Lebesgue-Radon-Nikod $\acute{y}$ m theorem for      318
Decomposition of a complex measure, Jordan      309
Decomposition of a finitely additive signed measure, Jordan      338
Decomposition of a measure space      317
Decomposition of a signed measure, Jordan      307
Decomposition theorem, Hahn      306
Decomposition theorem, Jordan      266
Decomposition theorem, Lebesgue      326
Decreasing function, strictly      105
Dedekind cut in an ordered field      46
Dedekind, R.      22
Degenerate measure      127 186
Delta, Kronecker      11
Denjoy integral      299
Dense subset of a topological space      61
Dense subsets of $\mathfrak{L}_{p}$       197
Density character of a topological space      219
Density of a set with respect to a $\sigma$ -algebra      374
Denumerable set      22
Derivates, Dini      257
Derivative      257
Derivative of a signed measure      366
Derivative of an absolutely continuous measure      328
Derivative of an indefinite integral      275
Derivative, Lebesgue — Radon — Nikod $\acute{y}$ m      328
Derivative, left      257
Derivative, right      257
Derivative, symmetric      271

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