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The Resource Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource)

Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource)

Label
Lectures on Functional Analysis and the Lebesgue Integral
Title
Lectures on Functional Analysis and the Lebesgue Integral
Statement of responsibility
by Vilmos Komornik
Creator
Subject
Language
eng
Summary
This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Komornik, V
Dewey number
  • 223
  • 515.7
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Universitext,
  • Springer eBooks
http://library.link/vocab/subjectName
  • Mathematics
  • Approximation theory
  • Functional analysis
  • Measure theory
Label
Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4471-6811-9
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
Some papers of general interest -- Topological prerequisites -- Part 1 Functional analysis -- Hilbert spaces -- Banach spaces -- Locally convex spaces -- Part 2 The Lebesgue integral -- Monotone functions -- The Lebesgue integral in R -- Generalized Newton-Leibniz formula -- Integrals on measure spaces -- Part 3 Function spaces -- Spaces of continuous functions -- Spaces of integrable functions -- Almost everywhere convergence -- Hints and solutions to some exercises -- Bibliography -- Teaching remarks -- Subject index -- Name index
Control code
978-1-4471-6811-9
Dimensions
unknown
Extent
1 online resource (XX, 403 pages)
File format
multiple file formats
Form of item
  • online
  • 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
9781447168119
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4471-6811-9
Other physical details
46 illustrations.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)951606554
Label
Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4471-6811-9
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
Some papers of general interest -- Topological prerequisites -- Part 1 Functional analysis -- Hilbert spaces -- Banach spaces -- Locally convex spaces -- Part 2 The Lebesgue integral -- Monotone functions -- The Lebesgue integral in R -- Generalized Newton-Leibniz formula -- Integrals on measure spaces -- Part 3 Function spaces -- Spaces of continuous functions -- Spaces of integrable functions -- Almost everywhere convergence -- Hints and solutions to some exercises -- Bibliography -- Teaching remarks -- Subject index -- Name index
Control code
978-1-4471-6811-9
Dimensions
unknown
Extent
1 online resource (XX, 403 pages)
File format
multiple file formats
Form of item
  • online
  • 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
9781447168119
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4471-6811-9
Other physical details
46 illustrations.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)951606554

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