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Thomson B.S. — Real Functions

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Название: Real Functions

Автор: Thomson B.S.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 229

Добавлена в каталог: 31.10.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(S)-\bar{D} f(x)$ (derivate)      14
$(S)-\Lambda(f, x)$ (cluster set)      3
$(S)-\lim inf_{y\rightarrow x}$       3
$(S)-\lim sup_{y\rightarrow x}$       3
$(S)-\lim_{i\rightarrow x}$ (interval function limit)      3
$(S)-\lim_{y\rightarrow x}$ (point function limit)      3
$(x^{\alpha})$ -porosity      197
      105 122
$C(\psi)$       125 157—160 203—205
$EXP(I, \psi)$       187
-property      72
-property      55 72 195
-property      195
,       185
$PI_{\psi}(E; x)$       197
      5
$S-\mu\psi$       41
(dual system)      7
      3—4
      5
$S_1\ll S_2$       5
$S_1\vee S_2$       5
$S_1\wedge S_2$       5
      21
      19
$S_{wap}$       22
$S_{\infty}$       3—4
$S_{\tau}$       18
$V(\psi, S;X)$       39
$Var(\psi, C)$       38
$VarK(\psi, C)$       41
$VK(\psi, S;X)$       41
      10 48—50
      29
      81
      82
$[Z_{\lambda}]$       127—129 150
$\bar{D}apf(x)$ , $\underline{D}apf(x)$ (approximate derivates)      15
$\bar{D}f(x)$ , $\underline{D}f(x)$ (bilateral derivates)      15
$\bar{D}Nf(x)$ , $\underline{D}Nf(x)$       15
$\bar{D}^#f(x)$ , $\underline{D}^#f(x)$ (sharp derivates)      15
$\bar{D}^+f(x)$ , $\underline{D}^+f(x)$ (Dini derivatives)      15
$\bar{\mathbb{R}}$       see “Extended real numbers”
$\Delta f$       39
$\lambda f$ (Lebesgue — Stieltjes measure)      96
$\lambda(E, x, y)$       184
$\Lambda(f, x)$       45
$\Lambda\ess(f, x)$       46
$\Lambda^+(f, x)$ , $\Lambda^-(f, x)$       45
$\mathbb{R}$       see “Real numbers”
$\psi$ -porosity      197
$\psi$ -porosity index      197
$\sigma$ -porous      55 65—66 184 189—190
$\sigma$ -strongly-porous      185
$\sigma-(S)$ -negligible      51 53
$\sigma-(\psi)$ -porosity      200
(S)-cluster set      3
(S)-continuous      70 89
(S)-cover      35—38 40 41
(S)-derivedset      50
(S)-limit      3
(S)-negligible      51
Absolutely continuous      105—106
ACG      129
Ambiguity theorem      44 62
Approximate bilateral derivate      134
Approximate continuity      73 148
Approximate derivative      24 155 160 162—165
Approximate Dini derivatives      15 24 129 135—136 139 145 147—150 153 155 170—175
Approximate system      22
Approximately constant      118—119
Approximately increasing      117—119
Approximately oscillatory      118—119
Asymmetry theorem      44 56 60—62
Baire 1 function      16 72 74—77 80 90 137 196
Baire 2 function      52
Baire property      79
Beppo Levi Theorem      143
Bilateral      37
Bilateral approximate derivate      24
Bilateral derivates      14
Bilaterally increasing      115—116
Bilaterally strongly porous      184
Cantor set      64—65 206 210
Cauchy — Schwartz inequality      111
Closure operator      19—21 47 56
Cluster set      3 6 24 44—69 183
Congruent system      25 162—163
Cover      35
d(x, l)      185
Darboux function      77
Denjoy — Khintchine theorem      160
Denjoy — Young — Saks theorem      139 166—182
Density system      22—24 27—28 31 33—34 52 54
Density topology      19 23
Derived set      50
Dini derivatives      15 122 135 138 166 115
Dual properties      10
Dual system      7
Essential asymmetry      64—67

Essential cluster set      44 46 64 76—69
Evans — Humke porosity lemma      191
Evans — Humke theorem      158—160
Extreme bilateral derivates      14
Extreme derivates      14
Feeble continuity      53 70
Filtering      10
Finite variation      39 86 90—96 110
Full cover      35
Full measure system      25
Goldowsky — Tonelli theorem      137
Guage      32
Hausdorff measure      202—203
Increasing sets property      41—43
Intersection condition      31—37 74 88 91 101—121 128—129 143—145 151 158 162
Joint intersection condition      59—61 63—64
Jordan decomposition      92
Lattice      5
Lebesgue decomposition      93
Lebesgue Stieltjes measure      96 100 105
Local system      3
Locally increasing      115
Measure continuous      78
Metric outer measure      40
Monotonicity property      131
Mutually singular functions      110—114
N-continuous      72
Nearly continuous      78
Negligent cluster set      62
Negligent continuity      78—80
Negligent Dini derivatives      22 129 136 145—146 150 179—182
Negligent limits      21—22
Nonporous      184
Outer measure      40
Partial order      5
Path generated      30
Path limit      27—31
Path system      25 30
Porosity      26 55 65 72 119 123—127 139 148 151 153 155—157 158—160 161 163 172—177 179—182 183—211
Porosity derivate      194
Porosity derivates      26 161
Porosity function      197
Porosity index      185
Porosity lemma      191—194 203—205
Porosity system      26
Porous      184
Positive measure system      24 46 67
Preponderant continuity      73
Qualitative continuity      78
Qualitative Dini derivatives      22 179
Quasi limit      26 82
Relative monotonicity      115 120—130
S (local system)      3
Saks — Sierpinski theorem      101
SAP      22
Selective system      26
Semicontinuous      71 74
Sequential derivative      164—165
Sequential system      25
Sharp derivates      15 138 151 154—155 178
Simply approached      44—45
Singular function      108—114
Sn      21
Stieltjes measure      39 85
Strict limit      12—13
Strongly porous      184
Swap      22
Symmetric perfect set      205—211
Theorem of Beppo Levi      138 143 147
Theorem of Burkill      136
Theorem of de la Vallee Poussin      106
Theorem of Denjoy — Khintchine      160
Theorem of Denjoy, Young and Saks      166—182
Theorem of Evans — Humke      158—161
Theorem of G.C. Young      138 143 146—147
Theorem of Goldowski and Tonelli      137
Theorem of Humke and Preiss      211
Theorem of O’Malley      136
Theorem of Saks and Sierpinski      101
Theorem of Titchmarch and Aumartn      135
Theorem of Vitali      96—98 167 170
Theorem of W.H. Young      138 151—155 160 178
Theorem of Wazewski      135
Tkadlec measure      211
u-derivative      19
Ultrafilters      11
Variation      38 85—114
Variationally equivalent      39 86—87 92 104
VBG      95 122
VBG*      93—95 97—98 103—104 106—107 113 115 122 130 134
Vitali cover      36
Vitali theorem      96—98 167 170
W.H. Young theorem      138 151—155 159 178
Weak approximate system      22
Weakly approximately continuous      54
Weakly approximately increasing      117—119
Weakly N-approached      47
Weakly N-continuous      54 73
Zahorski derivate      194
Zero variation      39 86
[VBG]      95

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