The Resource Integration and modern analysis, John J. Benedetto, Wojciech Czaja
Integration and modern analysis, John J. Benedetto, Wojciech Czaja
Resource Information
The item Integration and modern analysis, John J. Benedetto, Wojciech Czaja represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Integration and modern analysis, John J. Benedetto, Wojciech Czaja represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 DieudonnéGrothendieck 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: * Indepth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of stateoftheart results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of selfsimilarity 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 HahnSaks; * 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 selfstudy
 Language
 eng
 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
 SelfSimilar Sets and Fractals
 Functional Analysis
 Fourier Analysis
 Isbn
 9781280384172
 Label
 Integration and modern analysis
 Title
 Integration and modern analysis
 Statement of responsibility
 John J. Benedetto, Wojciech Czaja
 Subject

 Functions of real variables
 Functions of real variables
 Integrals, Generalized
 Integrals, Generalized
 Integrals, Generalized
 Integration, Functional
 Integration, Functional
 Integration, Functional
 Mathematical analysis
 Mathematical analysis
 Mathematical analysis
 Measure theory
 Measure theory
 Measure theory
 Functions of real variables
 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 DieudonnéGrothendieck 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: * Indepth development of measure theory and Lebesgue integration; * Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of stateoftheart results; * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of selfsimilarity 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 HahnSaks; * 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 selfstudy
 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
 Bibliography note
 Includes bibliographical references (pages 529550) 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  SelfSimilar 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
 10.1007/9780817646561
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817643065
 Publisher number
 10888298
 Specific material designation
 remote
 System control number
 (OCoLC)535009520
 Label
 Integration and modern analysis, John J. Benedetto, Wojciech Czaja
 Bibliography note
 Includes bibliographical references (pages 529550) 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  SelfSimilar 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
 10.1007/9780817646561
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817643065
 Publisher number
 10888298
 Specific material designation
 remote
 System control number
 (OCoLC)535009520
Subject
 Functions of real variables
 Functions of real variables
 Integrals, Generalized
 Integrals, Generalized
 Integrals, Generalized
 Integration, Functional
 Integration, Functional
 Integration, Functional
 Mathematical analysis
 Mathematical analysis
 Mathematical analysis
 Measure theory
 Measure theory
 Measure theory
 Functions of real variables
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/IntegrationandmodernanalysisJohnJ./6f8uTDLNGlA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/IntegrationandmodernanalysisJohnJ./6f8uTDLNGlA/">Integration and modern analysis, John J. Benedetto, Wojciech Czaja</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>