Wheeden R.L., Zygmund A. — Measure and integral. An introduction to real analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Wheeden R.L., Zygmund A. — Measure and integral. An introduction to real analysis

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Название: Measure and integral. An introduction to real analysis

Авторы: Wheeden R.L., Zygmund A.

Аннотация:

The book presupposes that the reader has a feeling for rigor and some knowledge of elementary facts from calculus. Some material which is no doubt familiar to many readers has been included; its inclusion seemed desirable in order to make the presentation clear and self-contained.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 274

Добавлена в каталог: 07.11.2005

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Предметный указатель

Measure space      162
Measure zero      167
Metric      132
Metric outer measure      196
Metric space      2 132
min (minimum)      4
Minkowski's inequality for integrals      129 173
Minkowski's inequality for series      131
Minkowski's integral inequality      143
Modulus of continuity      14 220
Modulus of continuity in $L^{p}$       221
Monotone Convergence Theorem      66 75 172
Monotone decreasing or increasing      9
Mutually singular measures      180
n-dimensional cube      7
n-dimensional Euclidean space      1
n-dimensional interval      7
Negative part of $\chi$       18
Negative variation of a function      18
Nonmeasurable set      46
Nonoverlapping intervals      7 8
Nontangential Abel summability      232 248
Norm in $L^{p}$       132
Norm in a Banach space      131
Norm of a bounded linear functional      182
Norm of a partition      12 16
Normed linear space      131
Null set      191
Odd function      214
Odd part of a function      223
Open ball      5
Open cover      8
Open interval      7
Open set      5
Order of a trigonometric polynomial      216
Origin      1
Orthogonal set of functions      135 211 213
Orthonormal set of functions      135 211
Outer measure Caratheodory      196
Outer measure general      193
Outer measure Hausdorff      202
Outer measure Lebesgue      33
Outer measure Lebesgue — Stieltjes      199
Outer measure metric      196
Outer measure regular      199
Parallelepiped      7
Parallelogram law      144
Parseval's formula      138 212 219
Partition      15
Partly open interval      6
Perfect set      6
Point of density      107
Point of dispersion      107
Point of the Lebesgue set      108
Poisson integral      151 247
Poisson kernel      151 247
Positive part of $\chi$       18
Positive summability matrix      231
Positive variation of a function      18
Principal value integral      239
Property $\mathscr{C}$       57
Property $\mathscr{F}$       88
pth modulus of continuity      221
Radon — Nikodym theorem      180
Real-valued function      9
Rectifiable curve      21
Refinement of a partition      17
Region under f      64
Regular Borel measure      187 208
Regular discontinuity      224
Regular outer measure      199
Regular shrinking of sets      108
Relation of convergence in measure and pointwise convergence      59 60
Relation of Riemann and Lebesgue integrals      83
Relation of Riemann — Stieltjes and Lebesgue integrals      76
Relation of Riemann — Stieltjes and Lebesgue — Stieltjes integrals      201
Relation of two definitions of the Riemann-Stieltjes integral      29 30
Relative complement of a set      2
Relatively closed (open) set      6
Removable discontinuity      10
Riemann integral      12 85
Riemann — Lebesgue lemma      144 220
Riemann — Stieltjes integral      23
Riemann — Stieltjes sums      23 27
Schur's lemma      60
Schwarz's inequality      3 128 141

Semicontinuous function      55 197
Separable      4 132 174
Sequence of points      3
Sequence of sets      2 165
Set Borel      40 196
Set Cantor      35
Set closed      5
Set compact      8
Set function      98 162
Set function absolutely continuous      99 174
Set function decomposition of      165 178
Set function singular      174
Set function variations of a      164
Set measurable      37 162 193
Set nonmeasurable      46
Set of type $A_{\delta},A_{\sigma}, G_{\delta}, G_{\sigma}$       6
Set open      5
Set perfect      6
Shrink regularly      108
Sign $\chi$       129
Simple function      54
Simple Vitali lemma      102
Singular function of a real variable      116
Singular measure      180
Singular set function      174
Smallest $\sigma$ -algebra containing $\mathscr{C}$       40
Space $L^{p}$       125 173
Space Banach      131
Space Hilbert      141
Space measure      162
Space metric      2 132
Space normed linear      131
span      137
Step function      23
Strictly monotone function      9
Subalgebra      209
Subcover      8
Sublinear operator      160
Summability Abel      231 246
Summability by arithmetic means      231 235
Summability nontangential Abel      232 248
Summability of a sequence      231
Summability of a series      231
Sup (supremum)      4
Support of a function      9
Supporting line      122
Symmetric derivative      248
Symmetric difference      190
Tauber's theorem      233
Tchebyshev's inequality      68 82
Tietze extension theorem      14
Tonelli's theorem      92
Total variation of a set function      164
Transformation      10
Transformation Lipschitz      44
Translation invariant      48
Triadic (ternary) expansion      47
Triangle inequality      3
Trigonometric Fourier series      211
Trigonometric polynomial      216
Trigonometric series      216
Trigonometric system      213
Type $A_{\delta}, A_{\sigma}, F_{\sigma}, G_{\delta}$       6
Uniform convergence theorem      75 172
Uniformly absolutely continuous      124 192
Uniformly bounded      9
Uniformly continuous      11
union      2
Upper Riemann — Stieltjes sum      27
Upper semicontinuous      55 197
Upper variation of a set function      164
Urysohn's lemma      192
Variation, bounded      15
Variations of a function      15 18
Variations of a set function      164
Vector      1
Vitali Covering Lemma      109
Vitali covering lemma simple form of      102
Vitali's theorem      46
Volume of an interval (parallelepiped)      7
Weak $L(\mathbf{R}^{n})$       105 250
Weak convergence      144
Weierstrass approximation theorem      238
Young's convolution theorem      146
Young's inequality      127
Zermelo's axiom      46

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