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Kurtz D.S., Swartz C.W. — Theories of Integration |
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Предметный указатель |
# 74
80
6
123 244
39
68
120
80
120
28
117
28
117
33
38
21
11
90
90
123
60
244
64
20
84
81
44
45
141 207 224
7 11
20
172
172
39
136
38
22
12
-fine free tagged partition 224
-fine tagged partition 140 156 207
51
12 141 208 225
31 99
97
12 141
85
80
172
218
72
73
84
73
73
205
68
240
84
7 11
38
111 1237
8060
-algebra 69
136
22
28
28
a.e. 42
Abel's Test 217
Absolutely continuous 106 202
Absolutely convergent 115
Absolutely integrable see Riemann
Absolutely integrable, integrable see Lebesgue integrable see see
Additivity condition 33
Alexiewicz semi-norm 205
Algebra 69
Almost all 89
Almost every 89
Almost everywhere 42 89
Archimedes 2
Ball 80
Borel measure 77
Borel sets 72
Bounded 80
Bounded convergence theorem 110 188
Bounded variation 172
Brick 80
Canonical form 86
Cantor set 79
Cantor set, generalized 79
Caratheodory 64
Cauchy 6
Cauchy criterion 19 150 228
Cauchy principal value 44 45
Cauchy sequence 123
Cauchy sum 6
Cauchy — Riemann integrable 42 44
Cauchy — Riemann integrable, conditionally 46
Cauchy — Schwarz inequality 127
Change of variables 37
Characteristic function 12
Closed 80
Closure 38
Compact 80
Comparison Test 45 170
complete 123
Conditionally integrable 161 see
Converge 42 80 123
Countable additivity 60
Countably additive 73 74
Countably subadditive 61
Counting measure 74
d(F) 40
d(I,J) 64
Darboux 20
Darboux integrable 22
Darboux sum, lower 20
Darboux sum, upper 20
Dedekind's Test 179
Denjoy 135
Dense 131
Derivative, lower 136
Derivative, upper 136
Dirichlet function 14
Discrete metric 122
Distance 80
Distance from I to J 64
Distance-1 metric 122
diverge 42
Dominated Convergence Theorem 110 187 239
E + h 61
Egoroff 90
| Even function 47
Extended real numbers 85
Extended real-valued function 86
Fatou 109
Fatou's lemma 109 186 239
Fischer 123
Free tagged partition 224
Free tagged subpartition 228
Fubini 117
Fubini’s Theorem 118 213 256
Fundamental Theorem of Calculus: Part I 34 134 143 190 232 see
Fundamental Theorem of Calculus: Part II 35 191 193 233
Gamma function 51
Gauge 140 156 207
Gauge integral 141
Generalized Fundamental Theorem of Calculus: Part I 148
Generalized Riemann integral 141
Henstock — Kurzweil integrable 141 156 208
Henstock — Kurzweil integrable, absolutely 147
Henstock — Kurzweil integral, indefinite 164 175 190 195
Henstock’s Lemma 163 229
Improper integral 42
Indefinite integral see Riemann integral see see
Inner measure 64
Integrable Darboux see Darboux integrable
Integrable Henstock — Kurzweil see Henstock — Kurzweil integrable
Integrable Lebesgue see Lebesgue integrable
Integrable McShane see McShane integrable
Integrable over E, Henstock — Kurzweil 194
Integrable over E, Lebesgue 103
Integrable over E, McShane 240
Integrable over E, Riemann 31
Integrable Riemann see Riemann integrable
Integration by parts 37 149
Integration by substitution 37
Interior 33
interval 80 207
Jordan content, outer 38
Lebesgue 56
Lebesgue integrable 103
Lebesgue integrable, absolutely 104
Lebesgue integral 97 99
Lebesgue integral, indefinite 203
Lebesgue measurable 68 83
Lebesgue measure 68 84
Lebesgue measure 0 41
LIMIT 123
Limit, inferior 90
Limit, superior 90
Linearity 15
Lipschitz condition 35
Lipschitz constant 35
Littlewood 92
Littlewood’s three principles 92
Lusin 93
M 68
Major function 136 245
Maximum 28
McShane integrable 224 254
McShane integrable, absolutely 229
McShane integral 254
Mean value theorem 48
Measurable function 86
Measurable set 64
Measure 74
mesh 7 11
Metric 122
Metric space 122
Mikusinski 113
Minimum 28
Minor function 136 245
Monotone 61
Monotone Convergence Theorem 100 104 181 184 236 238
Multiplier 171
Norm 80 122
Null set 41 68
Odd function 47
open 80
Operator 15
Oscillation 38
Outer measure 60 81
Partition 6 11 154 155 207
Perron 135
Perron integrable 136
Positivity 15 16 146 228
Probkme de la mesure des ensembles 60
Probkme d’intkgration 56
refinement 22
Regular inner 126
Regular outer 77
Riemann 7
Riemann integrable 12
Riemann integrable, absolutely 46
Riemann integral, indefinite 35 204
Riemann integral, lower 22
Riemann integral, upper 22
Riemann sum 7 141 207 224
Riemann — Lebesgue lemma 131
Riesz 123
Riesz — Fischer theorem 123 244
Sampling point 7
Semi-metric 122
Semi-norm 122
sgm 36
Signum function 36
Simple function 59 86
Step function 27 94
Straddle Lemma 138
Subpartit ion 163
Symmetric difference 80
Tag 139 155 207 224
Tagged partition 139 155 207
Tagged partition, free 224
Tagged subpartition 163
Tagged subpartition, free 228
Tchebyshev 102
Tchebyshev’s inequality 102
Test set 68
Tonelli 119
Tonelli’s Theorem 119 213 257
Translation 61
Translation invariant 61
v(I) 80
Variation 172
Variation, negligible 196
Vector lattice 29
Vector space 29
Vitali cover 198
Vitali Covering Lemma 199
Volume 80 207
x-section 120
y-section 120
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