Borrow it
Coverart for item
The Resource Integration and modern analysis, John J. Benedetto, Wojciech Czaja

Integration and modern analysis, John J. Benedetto, Wojciech Czaja

Creator
Contributor
Summary
A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the Dieudonné-Grothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinating historical commentary interwoven into the exposition; * Hundreds of problems from routine to challenging; * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; * Two significant appendices on functional analysis and Fourier analysis. Key Topics: * In-depth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; * Evolution of the Riesz representation theorem to Radon measures and distribution theory; * Deep results in modern differentiation theory; * Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn-Saks; * Thorough treatment of rearrangements and maximal functions; * The relation between surface measure and Hausforff measure; * Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study
Language
eng
Work
Publication
Extent
1 online resource (xix, 575 pages)
Contents
  • Classical Real Variables
  • Lebesgue Measure and General Measure Theory
  • The Lebesgue Integral
  • The Relationship between Differentiation and Integration on
  • Spaces of Measures and the Radon#x2013;Nikodym Theorem
  • Weak Convergence of Measures
  • Riesz Representation Theorem
  • Lebesgue Differentiation Theorem on
  • Self-Similar Sets and Fractals
  • Functional Analysis
  • Fourier Analysis
Isbn
9781280384172
Instance
Label
Integration and modern analysis
Title
Integration and modern analysis
Statement of responsibility
John J. Benedetto, Wojciech Czaja
Creator
Contributor
Subject
Language
eng
Summary
A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the Dieudonné-Grothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinating historical commentary interwoven into the exposition; * Hundreds of problems from routine to challenging; * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; * Two significant appendices on functional analysis and Fourier analysis. Key Topics: * In-depth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; * Evolution of the Riesz representation theorem to Radon measures and distribution theory; * Deep results in modern differentiation theory; * Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn-Saks; * Thorough treatment of rearrangements and maximal functions; * The relation between surface measure and Hausforff measure; * Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Benedetto, John
Dewey number
515.8
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA300
LC item number
.B455 2009
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Czaja, Wojciech
Series statement
Birkhäuser advanced texts
http://library.link/vocab/subjectName
  • Mathematical analysis
  • Functions of real variables
  • Integration, Functional
  • Integrals, Generalized
  • Measure theory
  • Functions of real variables
  • Integrals, Generalized
  • Integration, Functional
  • Mathematical analysis
  • Measure theory
Label
Integration and modern analysis, John J. Benedetto, Wojciech Czaja
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 529-550) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Classical Real Variables -- Lebesgue Measure and General Measure Theory -- The Lebesgue Integral -- The Relationship between Differentiation and Integration on -- Spaces of Measures and the Radon#x2013;Nikodym Theorem -- Weak Convergence of Measures -- Riesz Representation Theorem -- Lebesgue Differentiation Theorem on -- Self-Similar Sets and Fractals -- Functional Analysis -- Fourier Analysis
Control code
535009520
Dimensions
unknown
Extent
1 online resource (xix, 575 pages)
Form of item
online
Isbn
9781280384172
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4656-1
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4306-5
Publisher number
10888298
Specific material designation
remote
System control number
(OCoLC)535009520
Label
Integration and modern analysis, John J. Benedetto, Wojciech Czaja
Publication
Bibliography note
Includes bibliographical references (pages 529-550) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Classical Real Variables -- Lebesgue Measure and General Measure Theory -- The Lebesgue Integral -- The Relationship between Differentiation and Integration on -- Spaces of Measures and the Radon#x2013;Nikodym Theorem -- Weak Convergence of Measures -- Riesz Representation Theorem -- Lebesgue Differentiation Theorem on -- Self-Similar Sets and Fractals -- Functional Analysis -- Fourier Analysis
Control code
535009520
Dimensions
unknown
Extent
1 online resource (xix, 575 pages)
Form of item
online
Isbn
9781280384172
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4656-1
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-8176-4306-5
Publisher number
10888298
Specific material designation
remote
System control number
(OCoLC)535009520

Subject

Member of

Library Locations

    • Ellis LibraryBorrow it
      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012

Library Links

Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Missouri Libraries. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...