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Bartle R.G. — The Elements of Integration
Bartle R.G. — The Elements of Integration

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Название: The Elements of Integration

Автор: Bartle R.G.

Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 129

Добавлена в каталог: 20.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mu^*$-measurable set      100
$\sigma$-algebra      6
$\sigma$-algebra generated by a family of sets      7
$\sigma$-field      6
$\sigma$-finite measure      20
Absolute continuity      35 84
Absolute integrativity      42
Additivity, countable      4 19
Algebra of sets      96
Algebra, Borel      7
Algebra, extended Borel      8
Almost everywhere      22
Almost everywhere convergence      22 65
Almost uniform convergence      72 ff.
Archimedes      1
Banach space      60
Borel algebra      7
Borel measurability of continuous and monotone functions      9
Borel measure      20 104
Borel set      7
Borel — Stieltjes measure      20 105
Caratheodory extension theorem      101
Caratheodory, C.      100
Cauchy sequence, in $L_p$      58
Cauchy — Bunyakovskii — Schwarz inequality      57
Characteristic function      3 9
Charge      23
Combinations of measurable functions      9
Complete measure space      103
Complete normed linear space      58
Completeness theorem      59
Completion of a measurable space      25
Completion of Borel measure      110
Completion of measure      25
Complex-valued functions, integral of      49
Complex-valued functions, measurability of      13
Conjugate indices      57
Continuity, absolute      35 84
Convergence in $L_p$      58 66
Convergence in mean      66 ff.
Convergence, almost everywhere      22 65
Convergence, almost uniform      72 ff.
Convergence, dominated      44 75
Convergence, pointwise      65
Convergence, uniform      65
Countably additive      19
Countably subadditive      100
Counting measure      20
De Morgan laws      7
Decomposition of measures      80—95
Dominated Convergence Theorem      44 75
Egoroff's theorem      74
Endpoint of an interval      2
Equivalence of functions      54
Essentially bounded function      60
Eudoxos      1
Extended real numbers      5
Extension of measures      96—112
Fatou's lemma      33 39
Field      96
Frechet, M.      4
Fubini's theorem      119
Function measure      19
Function, characteristic      3 9
Function, complex valued      13
Function, continuous      9
Function, essentially bounded      60
Function, imaginary part of      14
Function, integrable      41
Function, measurable      8 10
Function, monotone      9
Function, negative part of      10
Function, positive part of      10
Function, real part of      14
Function, simple      3 27
Function, step      3 38
Function, summable      41
Functional, linear      59
Functional, representation of      90 ff. 106
Hahn decomposition theorem      81—82
Hahn extension theorem      103
Hahn, F.      103
Hoelder's inequality      56
Inequality, Cauchy — Bunyakovskii — Schwartz      57
Inequality, Hoelder      56
Inequality, Minkowski      57
Infimum      5
Integrable function      41
Integral of complex-valued functions      49
Integral of nonnegative measurable functions      30
Integral of nonnegative simple functions      28
Integral of real-valued integrable functions      41
Integral, indefinite      42
Integral, Riemann      3 38
interval      2
Joichi, T.J.      78—79
Jordan decomposition theorem      83
Lebesgue decomposition theorem      88
Lebesgue dominated convergence theorem      44
Lebesgue measure      20 104
Lebesgue spaces      52—64
Lebesgue — Stieltjes measure      105
Lebesgue, H.      1
Leibniz, G.W.      1
Length of an interval      3 96
Levi, B.      31
Limit of a sequence of extended real numbers      5
Limit of a sequence of sets      16
Linear functional      89 ff. 106
Mean convergence      66 ff.
Measurable function      8 10
Measurable set      7
Measurable space      6
Measure      19
Measure generated by a monotone function      20 105
Measure, $\sigma$-finite      20
Measure, absolute continuous      84
Measure, Borel      20 104
Measure, Borel — Stieltjes      20 105
Measure, construction of      96—112
Measure, counting      20
Measure, finite      20
Measure, Lebesgue      20 105
Measure, Lebesgue — Stieltjes      105
Measure, outer      99
Measure, singular      88
Measure, space      22
Measure, unit      20
Minkowski's inequality      57
Monotone class      17 18 116
Monotone class lemma      116
Monotone Convergence Theorem      31
Monotone function      9
Negative part      10
Negative set      80
Negative variation      82
Newton, I.      1
Nonmeasurable set      104
Norm      52
Norm of a linear functional      89
Normed linear convergence      68
Null set      80
Outer measure      99
Pointwise convergence      65
Positive part      10
Positive set      80
Positive variation      82
Product of two measures      115
Pseudo-norm      52
Radon — Nikodym derivative      87 94
Radon — Nikodym, theorem of      85 94 95
rectangle      113
Representation theorems of linear functionals      90 106
Riemann integral      3 38
Riemann, B.      1
Riesz representation theorem, on $L_1$      90 ff.
Riesz representation theorem, on $L_p$      91 ff.
Riesz representation theorem, on C      106 ff.
Riesz, F.      58 69 90—92 106—108
Rota, G.-C.      129
Schwarz inequality      57
Section      115
Semi-norm      52
Set, $\mu^*$-measurable      100
Set, Borel      7
Set, negative      80
Set, null      80
Set, positive      80
Simple function      3 27
Singular measure      6
Space measure      22
Space product      113
Space, measurable      6
Standard representation      27
Step function      3 38
Stieltjes — Lebesgue measure      105
Subadditivity, countable      100
Supremum      5
Theodore, R.      23
Theorem, Caratheodory extensions      101
Theorem, completeness      59
Theorem, dominated convergence      44
Theorem, Egoroff      74
Theorem, Fatou      33
Theorem, Fubini      119
Theorem, Hahn decomposition      81
Theorem, Hahn extension      103
Theorem, Jordan decomposition      83
Theorem, Lebesgue decomposition      88
Theorem, Lebesgue dominated convergence      44
Theorem, Levi monotone convergence      31
Theorem, monotone class      116
Theorem, monotone convergence      31
Theorem, product measure      114
Theorem, Radon — Nikodym      85
Theorem, Riesz representation      90 91 106
Theorem, Riesz — Fischer      59
Theorem, Tonelli      118
Theorem, Vitali convergence      76
Tonelli's theorem      118
Total variation      83
Truncation      16
Uniform convergence      65 ff.
Unit measure      20
Variation      25 82—83
Vitali convergence theorem      118
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