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Bridges D.S. — Foundations Of Real And Abstract Analysis |
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Предметный указатель |
-measurable 116
-norm 197
197
204
-adic metric 127
-power summable 196
-periodic 215
205
204
206
206
-approximation 149
Absolute convergence 31
Absolute value 15
Absolutely continuous 84
Absolutely convergent 180
Absorbing 282
Adjoint 254
Admissible array 305
Aggregate consumption set 303
Aggregate production set 303
Almost everywhere 85
Alternating Series Test 28
Antiderivative 69
antisymmetric 6
Approximate solution 230
Approximation theory 192
Ascoli's theorem 210
Associated metric 174
asymmetric 6
Attains bounds 149
Axiom of Archimedes 14 295
Axiom of Choice 299
Baire's theorem 279
Banach space 178
Beppo Levi's theorem 101
Bernstein polynomial 214
Bessel's inequality 245
Best approximation 192
Binary expansion 29
Binomial series 61
Bolzano - Weierstrass property 48
Bolzano - Weierstrass theorem 48
Borel set 113
Bound 184
Boundary 39
Bounded above 7
Bounded below 7
Bounded function 8
bounded linear map 183
Bounded operator 254
Bounded sequence 21 141
Bounded set 134
Bounded variation 71
Canonical bound 293
Canonical map 181
Cantor set 39
Cantor's theorem 26
Cauchy - Schwarz 126
Cauchy sequence 25 140
Cauchy-Euler method 230
Cauchy-Schwarz inequality 235
Centre 130
Ces ro mean 215
Chain 300
Chain connected 160
Chain rule 55
Change of variable 107
Characteristic function 99
Chosen point 304
Clarkson's inequalities 198
Closed ball 130
Closed graph theorem 285
Closed set 38 130 135
Closest point 192 239
Closure 38 130
Cluster point 38 130 135
Compact 146
Comparison Test 27
Competitive equilibrium 305
complete 26 140
Completion 142 179
complex numbers 19
conjugate 19
Conjugate bilinear 255
Conjugate exponents 194
Conjugate linear 234
Connected 158
Connected component 160
Consumer 303
Consumption bundle 303
Consumption set 303
continuous 44 136
Continuous on an interval 45
Continuous on the left 44
Continuous on the right 44
Continuously differentiable 223
Contraction mapping 220
Contraction mapping theorem 220
Contractive 136
Converge simply 206
Converge uniformly 206
Convergent mapping 138
Convergent sequence 20 139
Convergent Series 27 180
Convex 163 178
Convex hull 277
Coordinate 242
Coordinate functional 287
Countable 4
Countable choice 300
Countably infinite 4
Cover 47 146
Decreasing 8 101
Dense 132
Dependent choice 300
Derivative 53
Derivative, higher 54
Derivative, left 53
Derivative, right 53
Diameter 133
Differentiable 53
Differentiable -times 54
Differentiable on an interval 53
Differentiable, infinitely 54
Dini derivates 88
Dini's theorem 207
Dirichlet kernel 288
Dirichlet problem 257
Discontinuity 45 136
Discrete metric 126
Distance to a set 133
Divergence 256
Divergent series 28
Diverges 20
Dominated Convergence Theorem 104
Dominates 104
Dual 183
Edelstein's Theorem 149
Endpoint 19 163
Enlargement 155
equal 291 292
Equicontinuous 208
Equivalence class 6
Equivalence relation 6
Equivalent metrics 131
Equivalent norms 184
Essential supremum 204
Essentially bounded 204
Euclidean metric 127
| Euclidean norm 175
Euclidean space 127
Euler's constant 33
EXP 32
Exponential series 32
Extended real line 129
Extension, continuous 145
Extremal element 93
Extreme point 277
Extreme subset 277
Family 5
Farthest point 240
Fatou's lemma 104
Feasible array 305
Finite intersection property 148
Finite real number 129
First category 280
Fixed point 149 220
Fourier coefficient 242 288
Fourier expansion 248
Fourier series 215 288
Frontier 39
Fubini's Series Theorem 90
Function 3
Fundamental theorem of calculus 68 69
Gauss's divergence theorem 256
Geometric series 28
Glueing lemma 163
Gradient 256
GRAM - SCHMIDT 249
Graph 285
Greatest element 7
Greatest lower bound 7
Green's theorem 256
H lder's inequality 194 196 204
Hahn - Banach theorem 262
Hahn - Banach Theorem, complex 263
Heine - Borel - Lebesgue Theorem 47
Helly's theorem 277
Hermitian 254
Hilbert space 237
Hyperplane 187
Hyperplane of support 188
Hyperplane, translated 188
Idempotent 256
Identity mapping 136
Identity operator 240
Imaginary part 19
Increasing 8 101
Index set 5
Induced metric 131
Infimum 7
Infimum of a function 8
Infinitely many 20
Inner product 234
Inner product space 234
Integers 3
Integrable 95 98 234
Integrable over a set 99
Integrable set 113
integral 95 98
Integration by parts 109
Integration space 197
Interior 37 130 135
Intermediate value property 36
Intermediate Value Theorem 51 161
Interval of convergence 31
Interval, bounded 19
Interval, closed 19
Interval, compact 19
Interval, finite 19
Interval, half open 19
Interval, infinite 19
Interval, length of 19
Interval, open 18
Inverse mapping theorem 285
Irreflexive 5
Isolated 133
Isomet ry 128
Isometric 128
Iterates 220
Jacobi polynomial 252
Kernel 186
Korovkin's Theorem 212 215
Krein-Milman Theorem 277
L'H pital's rule 57
Landau's theorem 287
Laplacian operator 257
largest element 7
Laws of indices 16
Laws of logarithms 18
Least element 8
Least squares approximation 250
Least upper bound 7
Least-upper-bound principle 12
Lebesgue covering property 153
Lebesgue integrable 95
Lebesgue integral 95 98
Lebesgue measure 113
Lebesgue number 153
Lebesgue primitive 93
Lebesgue's Series Theorem 103
Left hand derivative 282
Legendre polynomial 252
lim inf 24
lim sup 24
Limit as tends to infinity 43
Limit Comparison Test 28
Limit inferior 24
Limit of a function 41
Limit of a mapping 138
Limit of a sequence 20 139
Limit point 48 138
Limit superior 24
Limit, left-hand 41
Limit, right-hand 41
Lindel f's Theorem 148
Linear functional 182
Linear functional, complex 259
Linear functional, extension of 261
Linear functional, real 260
Linear map 182
Lipschitz condition 143 219
Lipschitz constant 219
Locally compact 156
Locally connected 160
Locally nonsatiated 304
Logarithmic function 18
Lower bound 7
Lower integral 63 73
Lower limit 24
Lower sum 63 73
M ntz 216
Majorant 7
Majorised 7
Maximum element 7
Mazur's Lemma 270
Mean value theorem 57
Mean Value Theorem, Cauchy's 57
Measurable 110
Measurable set 113
Measure 113
Measure zero 80
mesh 62
Metric 125
Metric space 126
Metrisable 135
Minimum element 7
Minkowski functional 275
Minkowski's inequality 126 195 196 235
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