The Resource Advanced Integration Theory, by Corneliu Constantinescu, Wolfgang Filter, Karl Weber, (electronic resource)

Advanced Integration Theory, by Corneliu Constantinescu, Wolfgang Filter, Karl Weber, (electronic resource)

Label
Advanced Integration Theory
Title
Advanced Integration Theory
Statement of responsibility
by Corneliu Constantinescu, Wolfgang Filter, Karl Weber
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli­ cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de­ fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A
Member of
http://library.link/vocab/creatorName
Constantinescu, Corneliu
Dewey number
515.42
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • LH6kC5e8HNY
  • TmM5GPlk0ys
  • 0GmPqr7utCk
Image bit depth
0
Language note
English
LC call number
QA312-312.5
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Filter, Wolfgang.
  • Weber, Karl.
Series statement
Mathematics and Its Applications
Series volume
454
http://library.link/vocab/subjectName
  • Mathematics
  • Algebra
  • Distribution (Probability theory
  • Integral Transforms
  • Measure and Integration
  • Order, Lattices, Ordered Algebraic Structures
  • Real Functions
  • Probability Theory and Stochastic Processes
  • Integral Transforms, Operational Calculus
Label
Advanced Integration Theory, by Corneliu Constantinescu, Wolfgang Filter, Karl Weber, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references at the end of each chapters and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Suggestion to the Reader -- 0 Preliminaries -- Vector Lattices -- 1.1 Ordered Vector Spaces -- 1.2 Vector Lattices -- 1.3 Substructures, Quotients, Products -- 1.4 Bands and Orthogonality -- 1.5 Homomorphisms -- 1.6 The Order Dual of a Vector Lattice -- 1.7 Continuous Functionals -- 1.8 Order and Topology -- 1.9 Metric Spaces and Banach Spaces -- 1.10 Banach Lattices -- 1.11 Hilbert Lattices -- 1.12 Lattice Products -- Elementary Integration Theory -- 2.1 Riesz Lattices -- 2.2 Daniell Spaces -- 2.3 The Closure of a Daniell Space -- 2.4 The Integral for a Daniell Space -- 2.5 Systems of Sets, Step Functions, and Stone Lattices -- 2.6 Positive Measures -- 2.7 Closure, Completion, and Integrals for Positive Measure Spaces -- 2.8 Measurable Spaces and Measurability -- 2.9 Measurability versus Integrability -- 2.10 Stieltjes Functionals and Stieltjes Measures. Lebesgue Measure -- 3 Lp-Spaces -- 3.1 Classes modulo ?, and Convergence in Measure -- 3.2 The Hölder and Minkowski Inequalities and the Lp-Spaces -- 3.3 Lp-Spaces for 0< p< ? -- 3.4 Uniform integrability and the Generalized Lebesgue Convergence Theorem -- 3.5 Localization -- 3.6 Products and Lp? -- Real Measures -- 4.1 Nullcontinuous Functionals -- 4.2 Real Measures and Spaces of Real Measures -- 4.3 Integrals for Real Measures -- 4.4 Bounded Measures -- 4.5 Atomic and Atomless Measures -- The Radon-Nikodym Theorem. Duality -- 5.1 Absolute Continuity -- 5.2 The Theorem of Radon-Nikodym -- 5.3 Duality for Function Spaces -- 6 The Classical Theory of Real Functions -- 6.1 Functions of Locally Finite Variation -- 6.2 Real Stieltjes Measures -- 6.3 Absolutely Continuous Functions -- 6.4 Vitali?s Covering Theorem -- 6.5 Differentiable Functions -- 6.6 Spaces of Multiply Differentiable Functions -- 6.7 Riemann-Stieltjes Integrals -- Historical Remarks -- Name Index -- Symbol Index
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (XXIV, 876 p.)
File format
multiple file formats
Form of item
online
Isbn
9789400708525
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-94-007-0852-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000115719
  • (SSID)ssj0001295704
  • (PQKBManifestationID)11735847
  • (PQKBTitleCode)TC0001295704
  • (PQKBWorkID)11347076
  • (PQKB)10529528
  • (DE-He213)978-94-007-0852-5
  • (MiAaPQ)EBC3102489
  • (EXLCZ)993400000000115719
Label
Advanced Integration Theory, by Corneliu Constantinescu, Wolfgang Filter, Karl Weber, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references at the end of each chapters and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Suggestion to the Reader -- 0 Preliminaries -- Vector Lattices -- 1.1 Ordered Vector Spaces -- 1.2 Vector Lattices -- 1.3 Substructures, Quotients, Products -- 1.4 Bands and Orthogonality -- 1.5 Homomorphisms -- 1.6 The Order Dual of a Vector Lattice -- 1.7 Continuous Functionals -- 1.8 Order and Topology -- 1.9 Metric Spaces and Banach Spaces -- 1.10 Banach Lattices -- 1.11 Hilbert Lattices -- 1.12 Lattice Products -- Elementary Integration Theory -- 2.1 Riesz Lattices -- 2.2 Daniell Spaces -- 2.3 The Closure of a Daniell Space -- 2.4 The Integral for a Daniell Space -- 2.5 Systems of Sets, Step Functions, and Stone Lattices -- 2.6 Positive Measures -- 2.7 Closure, Completion, and Integrals for Positive Measure Spaces -- 2.8 Measurable Spaces and Measurability -- 2.9 Measurability versus Integrability -- 2.10 Stieltjes Functionals and Stieltjes Measures. Lebesgue Measure -- 3 Lp-Spaces -- 3.1 Classes modulo ?, and Convergence in Measure -- 3.2 The Hölder and Minkowski Inequalities and the Lp-Spaces -- 3.3 Lp-Spaces for 0< p< ? -- 3.4 Uniform integrability and the Generalized Lebesgue Convergence Theorem -- 3.5 Localization -- 3.6 Products and Lp? -- Real Measures -- 4.1 Nullcontinuous Functionals -- 4.2 Real Measures and Spaces of Real Measures -- 4.3 Integrals for Real Measures -- 4.4 Bounded Measures -- 4.5 Atomic and Atomless Measures -- The Radon-Nikodym Theorem. Duality -- 5.1 Absolute Continuity -- 5.2 The Theorem of Radon-Nikodym -- 5.3 Duality for Function Spaces -- 6 The Classical Theory of Real Functions -- 6.1 Functions of Locally Finite Variation -- 6.2 Real Stieltjes Measures -- 6.3 Absolutely Continuous Functions -- 6.4 Vitali?s Covering Theorem -- 6.5 Differentiable Functions -- 6.6 Spaces of Multiply Differentiable Functions -- 6.7 Riemann-Stieltjes Integrals -- Historical Remarks -- Name Index -- Symbol Index
Dimensions
unknown
Edition
1st ed. 1998.
Extent
1 online resource (XXIV, 876 p.)
File format
multiple file formats
Form of item
online
Isbn
9789400708525
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-94-007-0852-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000115719
  • (SSID)ssj0001295704
  • (PQKBManifestationID)11735847
  • (PQKBTitleCode)TC0001295704
  • (PQKBWorkID)11347076
  • (PQKB)10529528
  • (DE-He213)978-94-007-0852-5
  • (MiAaPQ)EBC3102489
  • (EXLCZ)993400000000115719

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