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
 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 Rd̂
 4 Spaces of integrable functions
 5 Integration on a product space
 6 Diffeomorphisms of open subsets of Rd̂ 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
 Dewey number
 515.42
 Index
 no index present
 LC call number
 QA312
 Literary form
 non fiction
 Nature of contents

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

 net
 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 Rd̂  4 Spaces of integrable functions  5 Integration on a product space  6 Diffeomorphisms of open subsets of Rd̂ and integration  7 Convolution  8 Complex measures  9 Harmonic analysis  10 Classical inequalities
 Control code
 ocn875182621
 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
 Other control number
 10.1007/9783034806947
 Quality assurance targets
 not applicable
 http://library.link/vocab/recordID
 .b31757789
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)875182621
 springer3034806949
Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.deakin.edu.au/portal/Acourseonintegrationtheoryincludingmore/mktRW9yhfFI/" typeof="CreativeWork http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.deakin.edu.au/portal/Acourseonintegrationtheoryincludingmore/mktRW9yhfFI/">A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.library.deakin.edu.au/#Deakin%20University%20Library"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.deakin.edu.au/">Deakin University Library</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.deakin.edu.au/portal/Acourseonintegrationtheoryincludingmore/mktRW9yhfFI/" typeof="CreativeWork http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.deakin.edu.au/portal/Acourseonintegrationtheoryincludingmore/mktRW9yhfFI/">A course on integration theory : including more than 150 exercises with detailed answers, by Nicolas Lerner</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.library.deakin.edu.au/#Deakin%20University%20Library"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.deakin.edu.au/">Deakin University Library</a></span></span></span></span></div>