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Kestelman H. — Modern theories of integration
Kestelman H. — Modern theories of integration

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Название: Modern theories of integration

Автор: Kestelman H.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd revised

Год издания: 1937

Количество страниц: 261

Добавлена в каталог: 20.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute continuity      188
Absolute continuity and bounded variation      189
Absolute continuity of $F\{\phi(x)\}$      193
Absolute continuity of integral      163 189
Accumulation      17
Aggregate      3 8 28
Almost all      36
Almost everywhere      36
Baire      25
Banach      vi 86
Base      94
Belongs      3
Bendixson      28
Bessel’s inequality      246
Borel      26
Bottom of cylinder      94
Bounded convergence      147
Bounded set      15
Bounded variation      185 187
Bounded variation and monotone functions      185 187
Bummabiiity of derivatives      174
Cantor      24 28 84
Carath$\acute{e}$odory      v
Cauchy — Lebesgue integral      213
Cauchy — Riemann integral      54 116 135
cell      32
Centre of interval      5
Centre of sphere      14
Closed envelope      18 19 20
Closed interval      5
Closed set      18
Cohen, L. W.      109
Complement      8
Complex function      156
Condensation      27
Contained      6
Content      32 57
Contiguous      20
continuous      31
Continuous function measurable      105
Convergence tests for Fourier series      236 237 238
Convergent sequence      21
coordinates      3
Corresponding point function      30
Cover      26
Covering theorems      26 85
cube      5
Cylinder      94
Darboux      40
Denjoy and Lebesgue integrals      220 223
Denjoy integral      218
Dense in itself      18
Derivate      172
Derivative of function of bounded variation      188
Derivative of monotone function      176 201
Derived set      18
Difference of sets      7
Differentiation of integral      45 46 173
Differentiation of series of monotone functions      176
Differentiation under integral sign      170
DIMENSION      3
Dini      237
Dirichlet’s kernel      233
Discontinuities of function integrable-$R$      37
Discontinuities of monotone function      163
Distance      14
Double integral      203
Element of set      3
Empty set      4
End-points      5
Enumerable      9
Envelope      18
Equal aggregates      6
Equivalent aggregates      9
Equivalent functions      139
Equivalent to a summable function      140
Estermann      vi 101 158
Exterior Jordan content      56
Exterior Lebesgue measure      67
Exterior measure of union      69 78
Fatou      124
Fej$\acute{e}$r      240
Finite aggregate      9
Fourier coefficients      229
Fourier series      229
Fraenkel      3 28
Fubini      176 203
Function of $P$      30
Gamma function      117 159 211
Gauge      32
Gauss      159
Greatest set of ordinates      92
H$\ddot{o}$lder — Lebesgue and Denjoy integrals      220
H$\ddot{o}$lder — Lebesgue integral      215
Half-space      75
Heine      26
Implies      4
Indefinite $D$-ntegral      219
Infinite aggregate      9
Infinity as real number      1
Integrable-$CR$      54
Integrable-$D$      219
Integrable-$H$      215
Integrable-$R$      33 36
Integral absolutely continuous      153 189
Integral continuous      162
Integration by parts      162 208
Integration by substitution      192
Integration of derivatives      46 174 178 180 183 224 226
Integration of Fourier series      241
Integration of limit functions      50 65 66 120 124 125 126 136 137 138 167
Integration of series      53 123 144 146 149 241
Interior      16
Interior Jordan content      56
Interior Lebesgue measure      81
Intersection of closed sets      20 24
Intersection of sets      6
interval      5
Inverse transformation      88
JORDAN      56 238
Jordan content      56 62 67 113
Least set of ordinates      92
Lebesgue and Cauchy — Riemann integrals      116 135
Lebesgue and Denjoy integrals      220 223
Lebesgue and Jordan measures      68 69 82
Lebesgue and Riemann integrals      115 130
Lebesgue exterior measure      71
Lebesgue integral      114 128 140 157
Lebesgue interior measure      81
Lebesgue measure      71
Limit of sequence      21
Limiting point      17
Lindel$\ddot{o}$f      26
Linear set      4
Linear transformation      87
Lower limit      100
Lower Riemann integral      33
Lower sum      33
Lusin      111
Maximum      30
Measurability of limit functions      102
Measurability of open set      77
Measurability of union and product      74 75
Measurable and continuous functions      109
Measurable and open sets      80
Measurable function      97
Measurable function as limit of bounded functions      108
Measurable set      71
Measurable-$J$      57
Measure      71
Measure additive      73
Minimum      30
Monotone function measurable      106
Mutually exclusive      6
Negative variation      185
Net      32
Non-enumerable sets      27 28
Non-measurable set      89
Non-summability      215
NULL      36
open      16
Ordinate sets      92 114 128
Origin      3
Oscillation      30 31
Parseval      245
Perfect set      18 25 84
Plane set      4
Point function      30
Point of $R_{n}$      3
Point of non-summability      215
Positive variation      18
primitive      46
Rational interval      5 13
Rational point      3 13
Real numbers      1
Regular points      214
Repeated and double integrals      205 208
Restricted linear transformation      87
Riemann and Lebesgue integrals      115 130
Riemann integral and Jordan content      55 62
Riemann — Lebesgue theorem      299
Riemrmn integral      33
Riesz — Fischer      244
Riesz, F.      199
Romanovski      v 217 218
Saks      v
Schwarz      152
Second mean-value, theorem      165
Section      9
Selection axiom      28 90
SEQUENCE      10
Set      4
Sierpi$\acute{n}$ski      28
Singular points      214
Space $R_{n}$      3
Special half-space      75
Sphere      14
Sub-aggregate      8
Sub-sequence      10
Subset      6
Substitution formula for integrals      161 192
Sum of sets      6
Summability ($C$, 1)      240
Summability of modulus      129 157
Summability of product      147 149 152
Summable function      114 119 129 131
Top of cylinder      94
Total variation      185
Transformation      87
Triangle theorem in $R_{n}$      14
Trigonometric series      228
Uniform convergence      52
Union of sets, upper limit      100
Upper Riemann integral      33
Upper sum      33
Vitali      85
Weierstrass      24
Zygmund      vi 181 232
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