Bridges D.S. — Foundations Of Real And Abstract Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Bridges D.S. — Foundations Of Real And Abstract Analysis

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Название: Foundations Of Real And Abstract Analysis

Автор: Bridges D.S.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 324

Добавлена в каталог: 13.12.2009

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

Предметный указатель

-measurable      116
$L_{p}$ -norm      197
$L_{p}(X)$       197
$L_{\infty}$       204
-adic metric      127
-power summable      196
$\alpha$ -periodic      215
$\mathcal{BV}(I)$       205
$\mathcal{B}(X, Y)$       204
$\mathcal{C}(X,Y)$       206
$\mathcal{C}^{\infty}(X,Y)$       206
$\varepsilon$ -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 $\grave{a}$ 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 $\ddot{o}$ 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 $\hat{o}$ 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 $\ddot{o}$ 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 $\ddot{u}$ 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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