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The Resource A Course on Integration Theory : including more than 150 exercises with detailed answers, by Nicolas Lerner, (electronic resource)

A Course on Integration Theory : including more than 150 exercises with detailed answers, by Nicolas Lerner, (electronic resource)

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
Contributor
Author
Subject
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 Carath{acute}eodory 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
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorDate
1953-
http://library.link/vocab/creatorName
Lerner, Nicolas
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Springer eBooks
http://library.link/vocab/subjectName
Mathematics
Label
A Course on Integration Theory : including more than 150 exercises with detailed answers, by Nicolas Lerner, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0694-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-0348-0694-7
Dimensions
unknown
Extent
XVIII, 492 pages 15 illustrations, 3 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034806947
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0694-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1058237140
Label
A Course on Integration Theory : including more than 150 exercises with detailed answers, by Nicolas Lerner, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0694-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-0348-0694-7
Dimensions
unknown
Extent
XVIII, 492 pages 15 illustrations, 3 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034806947
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0694-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1058237140

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