Dieudonne J.A. — Treatise on Analysis, Vol. 2 :: Электронная библиотека попечительского совета мехмата МГУ

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Dieudonne J.A. — Treatise on Analysis, Vol. 2

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Название: Treatise on Analysis, Vol. 2

Автор: Dieudonne J.A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 422

Добавлена в каталог: 09.12.2008

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Предметный указатель

Abel's partial summation formula      12.7 prob. prob.
Absolute continuity      13.15
Absolute value of a continuous operator      15.11 prob.
Absolute value of a measure      13.3
Absorbing set      12.13
Action of a group on a set      12.10
Adjoint of an element of an algebra with involution      15.4
Adjoint of an unbounded operator      15.12
Algebra with involution      15.4
Algebra without radical      15.2 prob.
Almost every where      13.6
Approximative point-spectrum      15.11 prob.
Atomic measure      13.18
Automorphism of a topological group      12.8
Baire's theorem      12.16
Balanced set      12.13
Banach algebra      15.1
Banach — Steinhaus theorem      12.16
Banach's principle      13.12 prob.
Banach's theorem      12.16
Barycenter      13.10 prob.
Bernoulli scheme      13.21 prob.
Bernstein polynomials      13.4 prob.
Beurling algebra      15.1 prob.
Beurling's theorem      15.11 prob.
Bieberbach's inequality      14.3 prob.
Birkhoff's Ergodic Theorem      13.9 prob.
Bitrace      15.7
Bochner — Godement theorem      15.9
Bohl's theorem      13.4 prob.
Borel — Cantelli theorem      13.21 prob.
Bounded above, below      12.7
Bounded complex measure      13.20
Bounded in measure      13.12
Bounded measure, bounded positive measure      13.9
Bounded real-valued function      12.7
Bounded subset (of a topological vector space)      12.14
Brunn — Minkowski inequality      14.2 prob.
Canonical extension of a measure      13.1
Canonical symmetry in a product      12.5
Canonical topology on a finite-dimensional vector space      12.13
Cantor's “diagonal trick”      12.5
Cap (in a convex set)      12.15 prob.
Carleman's criterion, Carleman's inequality      15.13 prob.
Cauchy sequence (in a metrizable topological group)      12.9
Cauchy — Schwarz inequality      13.11
Cauchy's determinant      13.11 prob.
Cayley transform of a hermitian operator      15.13
Centralizer of a subset of a group      12.8
Chacon — Ornstein ergodic theorem      13.17 prob.5
Chaotic topology      12.1
Character of an algebra      15.3
Characteristic function of a set      12.7
Choquet's theorem      13.10 prob.
Christoffel — Darbouxformula      15.13 prob.
Closed convex hull      12.14 prob.
Closed graph theorem      12.16
Closed unbounded operator      15.12
Closure of an unbounded operator      15.12
Coarser covering      12.6
Coarser partition      13.9 prob.
Coarser topology      12.1
Compact space      12.2 and 12.3 prob.
Comparable topologies      12.1
Compatible (topology and group structure)      12.8
Compatible (topology and vector space structure)      12.13
Complete additivity      13.8
Complete maximum principle      13.13 prob.
Complex measure      13.1
Compressible mapping      13.9 prob.
Condensation of singularities      12.16 prob.14
Conjugacy      15.13 prob.
Conjugate mappings preserving a measure      13.12 prob.
Conjugate of a complex measure      13.2
Continued fraction      13.14 prob.
Continuous almost everywhere      13.9 prob.
Convergence in mean, in square mean      13.11
Convergence in measure      13.2 prob.
Convergents to a continued fraction      13.14 prob.4
Convex hull      12.14 prob.
Convolution of a measure and a function      14.8
Convolution of two measures      14.5
Convolvable function and measure      14.8
Convolvable functions      14.10
Convolvable measures      14.5
Cotlar's lemma      15.4 prob.
Covering (G-)      14.1 prob.
Defect of an unbounded hermitian operator      15.13
Defined almost everywhere      13.6
Dense point, with respect to a measure-preserving transformation      13.11 prob.
Density with respect to a measure      13.1 and 13.13
Differentiation under the integral sign      13.8
Diffuse measure      13.18
Dirac measure      13.1
Directed set of seminorms      12.14
Dirichlet algebra      15.3 prob.
Dirichlet series      12.7 prob.
Discrete topology      12.1
Disjoint measures      13.18
Domain of an unbounded operator      15.12
Dominated Convergence Theorem      13.8
Dual of a locally convex space      12.15
Dunford — Schwartz ergodic theorem      13.21 prob.
EgorofTs theorem      13.9
Elementary set      12.5
entropy      13.9 probs. 28
Equi-integrable set      13.12 prob.
Equirepartitioned sequence      13.4 prob.
Equivalent functions      13.6
Equivalent measures      13.15
Equivalent representations      15.5
Equivalent seminorms      12.14
Ergodic mapping, measure      13.9 prob.
Ergodic point, with respect to a measure-preserving transformation      13.11 prob.
Ergodic set      13.11 prob.
Essential spectrum      15.13 prob.
Essential subspace      15.5
Essentially bounded function      13.12
Essentially self-adjoint unbounded operator      15.13
Exterior function      15.3 prob.
Extremal point      12.15 prob.
Faithful representation      15.5
Faithfully (group acting)      12.10
Farey series      13.14 prob.
Fatou's lemma      13.5
Filter base      12.3 prob.
Finer covering      12.6
Finer partition      13.9 prob.
Finer topology      12.1
Finite real-valued function      12.7
Fischer — Riesz theorem      13.11
Flight vector      12.15 prob.
Frechet space      12.14
Freely (group acting)      12.10
Fuglede's theorem      15.11 prob.
Fundamental sequence of partitions      13.9 prob.
Fundamental system of bounded subsets in a topological vector space      12.14 prob.
G-covering, -packing, -tessellation      14.1 prob.
Gauss — Kuzmin formula      13.14 prob.
Gelfand transformation      15.3
Gelfand — Mazur theorem      15.2
Gelfand — Neumark theorem      15.4
Gleason part      15.3 prob.
Group algebra      14.7
Group of real numbers modulo 1      14.2
Group with no small subgroups      12.9 prob.
Haar measure      14.1
Hahn — Banach theorem      12.15 prob.
Half-space      12.14 prob.
Hamburger's moment problem      13.20 prob.

Hardy spaces      15.3 prob. 16
Hardy — Littlewood maximal function      15.10 prob.
Hardy's inequality      13.11 prob.
Hausdorff space      12.3
Hausdorff's moment problem      13.4 prob.11
Hermitian character      15.4 prob.
Hermitian element (in an algebra with involution)      15.4
Hermitian unbounded operator      15.13
Hilbert algebra      15.7
Hilbert form      15.6
Hilbert sum of representations      15.5
Hilbert — Schmidt operator      15.4
Hoelder's inequality      13.11 prob.
Homogeneous space      12.11
Hopf's maximal ergodic theorem      13.11 prob.
Hyperextremal measure      15.3 prob.
Identity component of a topological group      12.8
Image of a measure      13.1 and 13.4 prob.
Incompressible mapping      13.9 prob.
Index of an operator      15.11 prob. prob.
Induced measure      13.1 and 13.9
Induced topology      12.2
Inequality of the mean      13.8 prob.
Infinite matrix      15.4
information      13.9 prob.
Inner measure of a set      13.5
Integrable function, set      13.7
Integral of a function over a set A      13.9
Integral of an integrable function      13.1 and 13.7
Integral with respect to a complex measure      13.16
Integration by parts      13.21 prob.
Interior function      15.3 prob.
Invariant measure (on a group)      14.1
Involution in an algebra      15.4
Irreducible idempotent      15.8
Isometric isomorphism of normed algebras      15.1
Isomorphism of topological groups      12.8
Isomorphism of topological vector spaces      12.13
Isoperimetric inequality      14.3 prob.
Jacob's theorem      12.15 prob.
Jacobi matrix      15.13 prob.
Jensen measure      15.3 prob.
Kac's theorem      13.11 prob.
Kakutani's skyscraper      13.9 prob.
Kernel      15.4 prob.
Khintchine's inequality      13.21 prob.
Khintchine's statistical recurrence theorem      13.11 prob.
KolmogororT — Sinai theorem      13.12 prob.10
Krein — Milman theorem      12.15 prob.
Krylov — Weinstein theorem      15.12 prob.
Lagrange's interpolation polynomial      12.16 prob.
Lagrange's theorem on sums of squares      14.2 prob.
Lebesgue function      13.16 prob.
Lebesgue measure      13.1
Lebesgue — Fubini theorem      13.21
Lebesgue — Nikodym theorem      13.15
Lebesgue's convergence theorems      13.8
Lebesgue's decomposition theorem      13.18
Left-invariant function on a group      12.9
Locally closed      12.2
Locally compact      12.2
Locally convex topological vector space      12.14
Locally finite family of subsets      12.6
Locally integrable function      13.13 and 13.16
Logmodular algebra      15.3 prob.
Lower envelope of a family of real-valued functions      12.7
Lower integral      13.5
Lower semicontinuous function      12.7
Lower semicontinuous regularization of function      12.7 prob.
Mahler's criterion      14.4 prob.
Majorized function      12.7
Majorized hermitian operator      15.13 prob.14
Marcinkiewicz's Theorem      13.21 prob.
Markoff — Kakutani theorem      13.4 prob.
Martingale (elementary)      13.9 prob.
Maximal ergodic theorem      13.9 prob.
Maximal ideal      15.3
Maximal in measure      13.12
Meager set      12.16
Measurable mapping, set      13.9 and 13.16
Measure      13.1
Measure concentrated on a subset      13.18
Measure defined by point masses      13.1
Measure of a set      13.7
Measure with base $\mu$       13.13
Mertens — Alexiewicz theorem      12.16 prob.12
Metrizable group      12.9
Metrizable space, topology      12.1
Minimum in measure      13.12
Minkowski area      14.3 prob.
Minkowski's inequality      13.11 prob.
Minkowski's theorem      14.2 prob.
Minorized function      12.7
Minorized hermitian operator      15.13 prob.14
Mixing mapping      15.11 prob.
Modulus function      14.3
Modulus of an automorphism      14.3
Moments of a measure      15.13 prob.
Muntz's theorem      13.11 prob.
Negligible function, subset      13.6 and 13.16
Neumark's theorem      15.11 prob.
Neutral component of a topological group      12.8
Nondegenerate representation      15.5
Normable algebra      15.1
Normal element of an algebra with involution      15.4
Normal unbounded operator      15.12
Normalized Haar measure      14.3
Normalizer of a subset      12.8
Normed algebra      15.1
Nowhere dense set      12.16
Nuclear operator      15.7 prob.
One-parameter subgroup      14.11 prob.
Open set      12.1
Opposite group      12.8
Orbit of a point under the action of a group      12.10
Orbit of a point under the action of monoid      12.15 prob.
Orbit space      12.10
Orthogonal projector      15.5
Orthornormal sequence of functions      13.11 prob.7
Outer measure of a set      13.5
p-adic integers      12.9 prob.
p-adic numbers      14.3 prob.
p-adic solenoid      12.9 prob.
Packing (G-)      14.1 prob.
Parallelotope      14.3
Partition of unity      12.6
Patching condition      12.2
Patching together of topological spaces      12.2
Plancherel — Godement theorem      15.9
Poincare's recurrence theorem      13.9 prob.11
Point-spectrum      15.12
Polar decomposition of an operator      15.11 prob.
Positive Hermitian operator      15.13 prob.
Positive linear form on an algebra with involution      15.6
Positive measure      13.2
Positive self-adjoint operator      15.11
Potential      13.13 prob.
Principle of domination      13.13 prob.
Product group      12.8
Product measure      13.21 and 13.21 prob.
Product of topological vector spaces      12.13
Product space, topology      12.5 and 12.5 prob.3
Proper mapping      12.7 prob.
Properly (group acting)      12.10 prob.
Pseudo-distance      12.4
Pure potential      13.13 prob.
Quadrable set      13.9 prob.
Quasi-ergodic set (with respect to an ergodic measure)      13.11 prob.
Quasi-invariant measure on a locally compact group      14.3 prob.
Quasi-nilpotent element in a Banach algebra      15.3 prob.

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