Vaeth M. — Volterra and integral equations of vector functions :: Электронная библиотека попечительского совета мехмата МГУ

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Vaeth M. — Volterra and integral equations of vector functions

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Название: Volterra and integral equations of vector functions

Автор: Vaeth M.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 349

Добавлена в каталог: 18.04.2005

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Предметный указатель

$\Delta_2$ -condition      72
$\gamma$ -bounded      20
$\gamma$ -bounded, countably      20
$\gamma$ -bounded, strictly      20
$\gamma$ -condensing      20
$\gamma$ -contracting      20
$\sigma$ -finite      38
$\theta$ -Volterra operator      99
(p, q)-exhaustion property      278
a.e.      36
a.e., B-sup-measurable      169
Algebraic semi-additive      19
Almost everywhere      36
Almost perfect      82
Associate space      85
Axiom of Choice      15 74 110 125 129 144 145 235
Axiom of choice, countable      15
Axiom of Dependent Choices      15
Axiom of dependent choices, $\omega$ -      143
B-bounded      186
B-equicontinuous      186
b-function      181
B-function, elementary      181
B-function, simple      181
B-function, strict      181
B-sup-measurable      169
B-sup-measurable, a.e.      169
Banach function space      63
Beppo Levi's theorem      83
Borel measure      60
Bounded with respect to $\gamma$       20
Bounded with respect to $\gamma$ , countably      20
Bounded with respect to $\gamma$ , strictly      20
Caratheodory condition      163
Caratheodory function      163
Caratheodory function, strict      169
Classical Predholm alternative      34 131
Closure point      127
Compact set, precompact      17
Compact set, relatively compact      17
Compactly generated, weakly      235
Compactness criterion, Krasnoselskii      78
Compactness criterion, Riesz      293
Condensing      20
Condensing, countably      20
Condition, $\Delta_2$ -      72
continuous      19
Continuum Hypothesis      15 60 178 248
Contracting with respect to $\gamma$       20
Contracting with respect to $\gamma$ , countably      20
Convergence, improper      68
Convergence, in finite measure      48
Convergence, in finite measure, topology      52
Convergence, in measure      48
Convergence, proper      69
Countable axiom of choice      15
Countably, bounded with respect to $\gamma$       20
Countably, bounded with respect to $\gamma$ , strictly      20
Countably, condensing      20
Countably, contracting with respect to $\gamma$       20
Decomposable in M      135
Dense      128
Dependent choices, axiomr      15
Dependent choices, axiomr, w-      143
Distance, Hausdorff      16
Dominated Convergence Theorem      81
Dominated convergence theorem, uniform      199
Dugundji's extension theorem      27 178
Egorov's theorem      46
Elementary function      58
Elementary function, B-      181
Elementary set      57
Elementary Uryson-measurable      215
Equicontinuous norm      71
Essentially separable valued      38
Exhausting sets      44
Exhaustion property      279
Exhaustion property, (p, q)-      278
Exhaustion theorem      44
Exhaustion theorem, for ideal spaces      70
Existence interval      128
Extendable at i      127
Extendable at i, family      132
Extendable at i, uniformly      132
Extendable at i, uniquely      127
Extension Principle      129
F-onto      156
Family      131
Fatou's lemma      83
Finite measure space      38
First uniform principle      133
Fixed point property      109
Fredholm alternative      34 131
Fredholm type      131
Fubini — Tonelli's theorem      58
Fubini's theorem      59
Function, B-      181
Function, B-, strict      181
Function, Caratheodory      163
Function, elementary      58
Function, elementary, B-      181
Function, integrable      53
Function, measurable      37
Function, simple      37
Function, simple, B-      181
Global solution for a partition sequence      155
Hausdorff distance      16
Hausdorff measure of noncompactness      17
Hausdorff measure of noncompactness, inner      17
Hoelder's inequality      86
Ideal space      63
Ideal space, real form      67
Ideal* space      66
Improper convergence      68
Inequality, Hoelder      86
Inequality, Minkowski      91
Inner Hausdorff measure of noncompactness      17
Inner regular      60
Integrable function      53
Integrally continuous      309
interval      127
Kernel      87
Koethe dual      85
Koethe space      63
Krasnoselskii's compactness criterion      78
Kuratowski measure of noncompactness      17
L-retraction property      234
Lattice measure of noncompactness      18
Lebesgue extension      36
Lebesgue's dominated convergence theorem      81
Lemma, Fatou      83
Lemma, Scorza — Dragoni      177
Localizable measure space      70
Locally invariant at $\theta$       109
Locally invariant at $\theta$ , uniformly      109
Locally solvable at $\theta$       107
Locally solvable at $\theta$ , uniformly      107
Locally solvable at i      135
Locally solvable at i, uniformly      135
Locally solvable at i, uniquely      135
Lorentz space      65
Luxemburg norm      65
Luxemburg — Gribanov theorem      86
Luzin's theorem      60
Majorant criterion      54
Marcinkiewicz space      65
Maximal solution      128
Measurable function      37
Measurable Uryson      214
Measurable Uryson, elementary      215

Measure bounded      183
Measure of noncompactness      19
Measure of noncompactness, Hausdorff      17
Measure of noncompactness, inner      17
Measure of noncompactness, Kuratowski      17
Measure of noncompactness, lattice      18
Minkowski's inequality      91
Mixed norm      86
Modulus of equicontinuity pointwise      253
Modulus of equicontinuity pointwise, uniform      253
Monotone      19
Monotone Convergence Theorem      83
Nonsingular      19
Normalized measure      38
Null set      36
Onto, F-      156
Operator, bounded with respect to $\gamma$       20
Operator, bounded with respect to $\gamma$ , countably      20
Operator, bounded with respect to $\gamma$ , strictly      20
Operator, condensing      20
Operator, contracting with respect to $\gamma$       20
Operator, Picard — Lindeloef      146
Operator, regular type      138
Operator, regular type, at $\theta$       117
Operator, triangular      106
Operator, Volterra      94 103
Operator, Volterra — Stieltjes      94
Operator, Volterra, $\theta$ -      99
Orlicz space      65
Partial integral operator      95
Partially additive      103
Partition      139
Perfect      83
Perfect, almost      82
Perfect, semi-      82
Picard — Lindeloef operator      146
Pointwise modulus of equicontinuity      253
Precompact      17
Preideal space      63
Preideal* space      66
Principle extension      129
Principle of dependent choices      15
Principle of dependent choices, w-      143
Principle, first uniform      133
Principle, second uniform      141
Proper convergence      69
Pseudometric      16
Quasinormed space      66
Real form of an ideal space      67
Regular ideal space      72
Regular linear integral operator      88
Regular measure of noncompactness      19
Regular part      72
Regular set      136
Regular type      138
Regular type, at $\theta$       117
Regular Uryson operator      182
Regular Uryson operator, uniformly      182
Relatively compact      17
Retraction property      234
Retraction property, L-      234
Riesz — Fischer property      82
Riesz' compactness criterion      293
Riesz' theorem      49
Scorza — Dragoni lemma      177
Second uniform principle      141
Semi-additive      19
Semi-homogeneous      19
Semi-perfect      82
Seminorm      168
Separable      16
Separable, measure space      53
Separable, valued, essentially      38
Simple function      37
Simple function, B-      181
Space, almost perfect      82
Space, associate      85
Space, Banach function      63
Space, ideal      63
Space, ideal*      66
Space, Koethe      63
Space, Lorentz      65
Space, Marcinkiewicz      65
Space, mixed norm      86
Space, Orlicz      65
Space, perfect      83
Space, preideal      63
Space, preideal*      66
Space, quasinormed      66
Space, real form      67
Space, regular      72
Space, semi-perfect      82
Strict B-function      181
Strict Caratheodory function      169
Strictly (T-) measurable      168
Strictly bounded with respect to $\gamma$       20
Strictly bounded with respect to $\gamma$ , countably      20
Summable      140
Sup-measurable, B-      169
Sup-measurable, B-, a.e.      169
Superposition operator      95
supp x      69
Support of a function      69
Support of a set      69
Symmetric difference      52
Theorem, Beppo Levi      83
Theorem, dominated convergence      81
Theorem, Dugundji      27 178
Theorem, Egorov      46
Theorem, exhaustion      44
Theorem, exhaustion, for ideal spaces      70
Theorem, Fubini      59
Theorem, Fubini — Tonelli      58
Theorem, Lebesgue      81
Theorem, Luxemburg — Gribanov      86
Theorem, Luzin      60
Theorem, monotone convergence      83
Theorem, Riesz      49
Theorem, Tonelli      59
Theorem, uniform      199
Theorem, Vitali      77
Theorem, Vitali, for ideal spaces      79
Tonelli's theorem      59
Topology of convergence in finite measure      52
Triangular operators      106
Uniform modulus of equicontinuity      253
Uniform principle, first      133
Uniform principle, second      141
Uniformly extendable at i      132
Uniformly extendable at i, family      132
Uniformly locally invariant at $\theta$       109
Uniformly locally solvable      141
Uniformly locally solvable at $\theta$       107
Uniformly locally solvable at i      135
Uniformly regular      182
Uniquely extendable at i      127
Uniquely locally solvable at i      135
Uryson operator      180
Uryson operator, regular      182
Uryson operator, regular, uniformly      182
Uryson-measurable      214
Uryson-measurable, elementary      215
Vitali's convergence theorem      77
Vitali's convergence theorem, for ideal spaces      79
Volterra operator      94 103
Volterra operator, $\theta$ -      99
Volterra — Stieltjes operator      94
Weakly compactly generated      235
Young function      65
Young function, generalized      67

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