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| Graves L.M. — Theory of Functions of Real Variables |
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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  , function of 78
Classes  and  of sets 175
Closed sequences in  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 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 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  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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