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

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
Creator
Author
Subject
Genre
Language
eng
Summary
This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov 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, change-of-variables 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 Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym 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
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-0348-0694-7
Instantiates
Publication
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
10.1007/978-3-0348-0694-7
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
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-0348-0694-7
Publication
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
10.1007/978-3-0348-0694-7
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)875182621
  • (OCoLC)ocn875182621

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