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The Resource A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner
A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner
Resource Information
The item A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the RieszMarkov Theorem and also via the Carathodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, changeofvariables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and HardyLittlewoodSobolev inequality, are proven. Further topics include the RadonNikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercises and detailed solutions. A comprehensive appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advanced material such as some basic properties of cardinals and ordinals which are useful for the study of measurability
 Language
 eng
 Extent
 1 online resource
 Contents

 1 Introduction
 2 General theory of integration
 3 Construction of the Lebesgue measure on R^d
 4 Spaces of integrable functions
 5 Integration on a product space
 6 Diffeomorphisms of open subsets of R^d and integration
 7 Convolution
 8 Complex measures
 9 Harmonic analysis
 10 Classical inequalities
 Isbn
 9783034806947
 Label
 A course on integration theory : including more than 150 exercises with detailed answers
 Title
 A course on integration theory
 Title remainder
 including more than 150 exercises with detailed answers
 Statement of responsibility
 by Nicolas Lerner
 Language
 eng
 Summary
 This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the RieszMarkov Theorem and also via the Carathodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, changeofvariables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and HardyLittlewoodSobolev inequality, are proven. Further topics include the RadonNikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercises and detailed solutions. A comprehensive appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advanced material such as some basic properties of cardinals and ordinals which are useful for the study of measurability
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 1953
 http://library.link/vocab/creatorName
 Lerner, Nicolas
 Dewey number
 515.42
 Index
 no index present
 LC call number
 QA312
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/subjectName

 Measure theory
 Integrals, Generalized
 Measure theory
 Integrals, Generalized
 Integrals, Generalized
 Measure theory
 Label
 A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 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
 1 Introduction  2 General theory of integration  3 Construction of the Lebesgue measure on R^d  4 Spaces of integrable functions  5 Integration on a product space  6 Diffeomorphisms of open subsets of R^d and integration  7 Convolution  8 Complex measures  9 Harmonic analysis  10 Classical inequalities
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783034806947
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783034806947
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)875182621
 (OCoLC)ocn875182621
 Label
 A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 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
 1 Introduction  2 General theory of integration  3 Construction of the Lebesgue measure on R^d  4 Spaces of integrable functions  5 Integration on a product space  6 Diffeomorphisms of open subsets of R^d and integration  7 Convolution  8 Complex measures  9 Harmonic analysis  10 Classical inequalities
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783034806947
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783034806947
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)875182621
 (OCoLC)ocn875182621
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/Acourseonintegrationtheoryincludingmore/wY1gkTuOw8E/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/Acourseonintegrationtheoryincludingmore/wY1gkTuOw8E/">A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>