Aliprantis C. — Principles of real analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Aliprantis C. — Principles of real analysis

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Название: Principles of real analysis

Автор: Aliprantis C.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-е издание

Год издания: 1998

Количество страниц: 424

Добавлена в каталог: 06.11.2012

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

Предметный указатель

$C^{1}$ -differentiable function      387
$C^{\infty}$ -function      203
$F_{\sigma}$ -set      61
$G_{\delta}$ -set      61
$L_{p}$ -norm      255
$L_{p}$ -space      255
$L_{\infty}(\mu)$ -space      261
$\ell_{2}$ -norm      305
$\epsilon$ -Cantor set      141
$\sigma$ -additivity      98
$\sigma$ -algebra generated by a collection      97
$\sigma$ -algebra generated by a family      150
$\sigma$ -algebra of sets      97
$\sigma$ -algebra product      154
$\sigma$ -compact set      357
$\sigma$ -finite measure space      113
$\sigma$ -finite set      116 175
$\sigma$ -finite signed measure      332
$\sigma$ -ring      150
$\sigma$ -set      94
$\Sigma$ -simple function      158
Absolute value      16
Absolute value of vector      67 243
Absolutely continuous function      380
Absolutely continuous measure      338
Absolutely summable series      223
Accumulation point      37 59
Addition of real numbers      14
Additive function      138
Additivity of set functions, $\sigma$       98
Additivity of set functions, finite      99
Adjoint of operator      242
Adjoint operator      297
Algebra of functions      89
Algebra of sets      95 150
Algebraic difference of sets      143
Algebraic number      13
Almost everywhere relation      120
Alternating series      33
Angle between vectors      282
Antisymmetry      7 66
Archimedean property      17
Archimedes (287-212 BC)      17 180
Area function      186 187
Arzela, Cesare (1846-1912)      75 188
Ascoli — Arzela theorem      75
Ascoli, Guido (1887-1957)      75
Associative laws      15
atom      120
Averaging operator      253
Axiom of Choice      7
Axiom of continuity      16
Axiom, completeness      16
Axioms, field      14
Axioms, order      15
Baire space      43
Baire's category theorem      44
Baire, Rene L. (1874-1932)      43
Balanced set      224
Ball, closed      36
Ball, open      35
Ball, unit      220
Banach lattice      246
Banach space      218
Banach space, reflexive      239
Banach — Mazur limit      241
Banach — Steinhaus theorem      229
Banach, Stefan (1892-1945)      217 218 229 232 237
Base      65
Base for topology      65
Basis, orthonormal      298
Bernoulli's inequality      14
Bernoulli, Jacob (1654-1705)      14
Bernstein polynomials      254
Bernstein, Felix (1878-1956)      12
Bernstein, Sergei N. (1880-1968)      254
Bessel, Friedrich W. (1784-1846)      283
Bessell's inequality      284
Binary relation      7
Bolzano, Bernard (1781-1848)      25 29
Borel measurable function      152
Borel measure      136
Borel measure, induced by a monotone function      373
Borel sets      97
Borel signed measure      362
Borel, Emile (1871-1958)      51
Bound, essential      260
Bound, lower      16
Bound, upper      16
Boundary of set      38 59
Boundary point      38 59
Bounded from above set      16
Bounded from below set      16
Bounded metric space      39
Bounded operator      225
Bounded set      16
Cancellation law of addition      19
Cancellation law of division      20
Cancellation law of multiplication      20
Cantor set      41 140
Cantor, Georg (1845-1918)      12 41
Caratheodory extension of measure      111
Caratheodory function      156
Caratheodory, Constantin (1873-1950)      103 107 111 156
Cardinal infinite      13
cardinal number      12
Cardinality of the continuum      13
Cartesian product      6
Cartesius (1596-1650)      6
Cauchy sequence      26 39
Cauchy sequence in measure      149
Cauchy sequence, uniform      71
Cauchy — Schwarz inequality      278
Cauchy, Augustin L. (1789-1875)      26 39 278
Cavalieri's principle      214
Cavalieri, Bonaventura (1589-1647)      214
cell      186
Chain      8
Chain rule      350
Change of variable      176
Change of variables formula      393
Characteristic function      126
Choice function      6
Circled set      224
Clopen set      65
Closed ball      36
Closed graph theorem      234
Closed mapping      52
Closed set      35 58
Closed unit ball      220
Closure of set      36 59
Closure point      36 59
Cluster point      23
Co-meager set      48
Commutative group      362
Commutative laws      15
Compact metric space      49
Compact operator      226
Compact set      49 62
Compact topological space      62
Complement of set      4
Complement, orthogonal      287 291
Complemented subspace      235
Complete metric space      39
Complete orthogonal set      293
Complete orthonormal set      298
Completeness axiom      16
Completion of a metric space      46
Complex inner product space      276
Complexification of a real vector space      277

Component of a point      48
Composition of functions      5
Condensation of singularities principle      230
Conjugate exponents      264
Connected metric space      47
Connected set      47
Connected topological space      65
Constant sequence      23
Continuous function      38 60
Continuous function at a point      60
Continuum      13
Continuum Hypothesis      13
Continuum hypothesis, generalized      13
Contraction      55
Convergence in measure      146
Convergence, pointwise      68
Convergence, uniform      69
Convergent sequence      22 37 60
Convergent sequence in mean      202
Convergent sequence in measure      146
Convergent sequence, weakly      365
Convergent series in a Banach space      223
Convex set      224
Countable set      9
Counting measure      99
Cover      48
Cover of set      48
Cover, measurable of a set      117
Cover, open      48
Cover, pointwise finite      56
Cylindrical coordinate transformation      395
Cylindrical coordinates      395
Daniell, P.J. (1889-1946)      166
Darboux, Jean-Gastin (1842-1917)      181
De Morgan's laws      4
De Morgan, Augustin (1806-1871)      4
Decomposition, Hahn      331
Decomposition, Jordan      333
Decomposition, Lebesgue      342
Decreasing function      372
Decreasing sequence      22
Decreasing sequence of functions      70
Dense subset      37 59
Density function      344
Density point      371
Derivative      386
Derivative of measure      367
Derivative, lower of measure      367
Derivative, Radon — Nikodym      344
Derivative, upper of measure      367
Derived set      37 59
Descartes, Rene (1596-1650)      6
Determinant      386
Determinant, Jacobian      386
Diameter of a set      39
Diffeomorphism      388
Difference of two numbers      20
Difference, algebraic of sets      143
Difference, set      2
Difference, symmetric      3
Differential operator      225 227
Differentiate function      386
Differentiate measure      367
Dini's theorem      70
Dini, Ulisse (1845-1918)      70
Dirac's measure      99
Dirac, Paul A.M. (1902-1984)      99
Dirichlet kernel      316
Dirlchlet, Johann P.G.L. (1805-1859)      71 316
Discrete distance      34
Discrete metric space      34
Discrete topology      58
Disjoint sets      2
Distance      34
Distance function      81
Distance of a point from a set      81
Distance, discrete      34
Distance, Euclidean      34
Distance, uniform      70
Distributive law      15
Distributive laws      3 4
Division      20
Division law for fractions      20
Domain of function      5
Double series      30
Dual order      244
Dynkin system      152
Dynkin, Eugene B. (1924-)      152
Egorov's theorem      125
Egorov, Dimitry R. (1869-1931)      124
Element of a set      2
Element, first      10
Element, least      10
Element, maximal      8
Elementary matrix      390
Empty set      2
Enumeration      9
Equality of sets      2
Equality of two functions      5
Equicontinuous set      75
Equivalence class      7
Equivalence relation      7
Equivalent distances      39
Equivalent norms      220
Equivalent sets      9
Essential bound      260
Essential supremum      260
Essentially bounded function      260
Euclid (ca 365-300 BC)      34
Euclidean distance      34
Euclidean norm      218
Eudoxus of Cnidus (ca 400-347 BC)      17
Even polynomial      90
Eventually true property      22
Family of generators for $\sigma$ -algebra      151
Family of sets      3
Family, pairwise disjoint      4
Fatou, Pierre J.L. (1878-1929)      171
Fejer kernel      317
Fejer, Leopold (1880-1959)      317 318
Field axioms      14
Finer partition      178
Finite additivity      99
Finite intersection property      55
Finite measure space      113
Finite set      9
Finite signed measure      332
Finite subset property      272
Finitely additive measure      102
First category set      43 59
first element      10
Fischer, Ernst G. (1875-1954)      258
Fisher, Ernst S. (1875-1954)      258
Fixed point      55
Fourier coefficients      299 310
Fourier coefficients of a function      309
Fourier series of a function      309
Fourier, Jean B.J. (1768-1830)      299
Fresnel integrals      199 215
Fresnel, Augustin J. (1788-1827)      199
Fubini's theorem      212
Fubini, Guido (1879-1943)      212 382
Function      5
Function measurable in a variable      155
Function of bounded variation      376
Function space      68
Function with compact support      85 201
Function, $C^{1}$ -differentiable      387
Function, absolutely continuous      380
Function, additive      138

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