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Graves L.M. — Theory of Functions of Real Variables
Graves L.M. — Theory of Functions of Real Variables

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Название: Theory of Functions of Real Variables

Автор: Graves L.M.

Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1946

Количество страниц: 300

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      24
Absolute continuity      187 203 257
Absolute continuity in the sense of Tonclli      257
Absolute convergence      108
Absolutely-uniform convergence      110
Accumulation point of a sequence      49 50
Accumulation point of a set      44 49
Accumulation point of functions      119 246
Additive classes      195
Additive function      174 196 197
Aggregate      7 42
Almost everywhere      182
Almost uniform convergence      183
Alternation of propositions      2
Antiderivative      90
Approximate convergence      236—237
Archimedean property      27 34
Ascoli’s Theorem      122
Asymptotic series      115
Baire’s classification of discontinuous functions      127 200
Bessel’s inequality      249
Biconditional of propositions      4
Bilinear functions      76
Bilinear operator      262
Bolzano      49
Borel theorem      51
Borel-measurable functions      200
Borel-measurable sets      196
Boundary point      44
Boundary point of a sheet      142
Bounded set      49
Bounded variation      202 267
Cantor      38
Cantor discontinuum      41 48
Cartesian product      9 40
Categorical set of postulates      17
Cauchy condition for convergence in the mean      243
Cauchy condition for existence of a limit      36 60
Cauchy condition for uniform convergence      99
Characteristic function      60 181
Class $C^{(m)}$, function of      78
Classes $\mathfrak{U}$ and $\mathfrak{G}$ of sets      175
Closed sequences in $\mathfrak{L}_2$      248
Closed set      45
Closure of a set      45
Compact set      119
Complement of a set      8 42
Complete linearly ordered sets      28
Complete sequences in $\mathfrak{L}_2$      248
Concave function      116
Conditional of propositions      2
Conjunction of propositions      2
Connected set      47
Continuous function      63
Continuous function of two variables      102
Continuum      47
Convergence by rows      113
Convergence in measure      236—237
Convergence in the mean      237
Convergence, absolute      108
Convergence, absolutely-uniform      110
Convergence, almost uniform      183
Convergence, unconditional      108
Convergence, uniform      98
Convergent Series      107
Convex set      47
Counter class      10 18
CURVES      48 211
Decimal sequence      38
Dedekind cuts      28
Dedekind property      28 37
Degenerate interval      174
Dense linearly ordered set      28
Denumerable      38
Derivate      73 204
Derivative      69 72
Derivative of limit functions      103 252
Derived set      45
Differential of a function of several variables      76
Dini’s theorem      121
Disjoint sets      42 174
Divergent series      107 115
Domain of a function      11 54
Egoroff’s theorem      184 239
Epsilon-neighbothood of a function      119
Epsilon-neighbothood of a point      43
Epsilon-neighbothood of a set      44
Equicontinuous functions      119
Equivalence relation      24
Equivalent sequences      38
Essentially bounded functions      183 186
Exceptional points      142 170
Existential quantifier      6
Extension of a function      116
Extensionaliy attainable properties      180
Exterior measure      88 197
Exterior point      44
Field      33
Fixed point      146 149
Frontier point      44
Fubini’s Theorem      218
Function      11 54
Function of accumulation      119
Function of class $C^{(m)}$      78
Function of intervals      174
Function of measurable sets      197
Function of singularities      269
Function, additive      174 196 197
Function, bilinear      76
Function, characteristic      60 181
Function, concave      116
Function, continuous      63
Function, derivate of      73
Function, differential of      76
Function, domain of      11 54
Function, equicontinuous      119
Function, essentially bounded      183 186
Function, extension of      116
Function, integrable      85 189 260 261 269 271
Function, limit of      56
Function, linear      75
Function, maximum and minimum of      65
Function, measurable      183
Function, nondifferentiable      125
Function, range of      11 54
Function, semicontinuous      63
Function, step      181
Function, summable      189
Function, uniformly continuous      66
Fundamental set of solutions      161
Greatest lower bound      28 57 62
Heine — Borel theorem      51
Holder condition      118
Holder’s Inequality      233
Identity      7
Implication      7
Indefinite integral      90 187
Infinity, axiom of      10
Infinity, points at      40
Integrable functions, in the sense of Lebesgue      189
Integrable functions, in the sense of Lebesgue in the sense of Riemann      85 194
Integrable functions, in the sense of Lebesgue in the sense of Stieltjes      260 261 269 271
Integral of differential equations      168
Integration by parts      94 220 265
Integration by substitution      94 221—227
Integration of limit functions      103 185 190 193 240 241 281—292
Interchange of order of differentiation      80
Interchange of order of repeated limits      100
Interior point      44
interval      41 174
Interval function      174
Isolated point      44
Jordan content      88
Jump function      268
Least upper bound      28 57 62
Lebesgue measure      88 195
Length of a curve      212
Limit point      44
Limited variation      202 267
Limits      36 49 56 236
Limits of a sequence of sets      42 43
Limits, lower and upper      57 58 62 98
Linear class of functions      119 181
Linear function      75
Linear operator      182 262 292
Linear order      21 27 28
Linear space      119
Lipschitz condition      118 136 203
Logical addition and multiplication      181
Logical laws      4
Lower bound      28 57 62
Lower integral      86 269
Lower limit      58 62 98
Lower semicontinuity      63
Mathematical induction      18 19
Matrix solution of linear differential equations      161
Maximum of a function      65
Mean-value theorems for derivatives      71 72 81
Mean-value theorems for integrals      96 231
Measurable function      183
Measure, exterior      88 197
Measure, Lebesgue      195
Measure, zero      88 178
Metric density      210
Minimum of a function      65
Minkowski’s inequality      234
Modulus of continuity      116
Mono tonic functions      56
Monotonic sequences      37
Moore theorem      100
Negation of a proposition      2
Neighborhood      43 44 119
Nondifferentiablc functions      125
Norm of a continuous function      119
Norm of a function in $\mathfrak{L}_p$      246
Norm of a point      76
Nowhere-dense set      46
Null class      8 42
Open set      45 177
Operations on classes      8 42 45
Ordered field      33
Ordinary point      142 170
Oscillation of a function      88
Oscillatory series      107 114
Parseval’s theorem      251
Partition      85 201 260
Peano postulates for the natural numbers      18 19
Perfect set      40
Point      40
Point of a set      44 49
Point of accumulation of a sequence      49 50
Point, exceptional      142
Point, ordinary      142
primitive      90
Range of a function      11 54
Regular sequences      36
Relative closure      46
Riesz — Fischer theorem      250
Riesz’ theorem      295
Rolle’s Theorem      70
Schwarz inequality      234
Separable sets      123
Sequences of numbers      36
Sequences of points      49
Sequences of sets      42 43
Sequences, decimal      38
Sequences, equivalent      38
Sequences, limits of      36 49
Sequences, monotonic      37
Sequences, regular      36
Sequences, satisfying Cauchy condition      36
Series      107
Series, asymptotic      115
Series, summability of      114
Set, bounded      49
Set, closed      45
Set, compact      119
Set, connected      47
Set, convex      47
Set, dense in another set      46
Set, dense in itself      46
Set, derivative      45
Set, measurable      195
Set, nowhere-dense      46
Set, open      45
Set, perfect      46
Set, relatively closed      46
Set, separable      123
Sheet of points      141 142
simplex      146
Simplicial partition      146
Solution of a differential equation      152
Step functions      181
Successive substitutions      134—136 152
Summability of series      114
Summable functions      189
Taylor’s Theorem      72 80 95
Theorem of the mean      71 72 81
Theorem of the mean for integrals      96 231
Tonelli, absolute continuity in the sense of      257
Total differential      76
Total variation      202 209
Transitive relations      21 25
Truth table      5
Unconditional convergence      108
Uniform approach to upper and lower limits      98
Uniform continuity      66
Uniform convergence      98
Universal quantifier      3 6
Upper bound      28 57 62
Upper integral      86 269
Upper limit      57 62 98
Upper semicontinuity      63 64
Variation of a function      202
Weierstrass      49
Weierstrass, approximation theorem of      123
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