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)
Resource Information
The item Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a nontraditional 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, clearcut versions of the classical theorems of FubiniTonelli and RadonNikodým. 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.
 Language
 eng
 Extent
 1 online resource (XX, 403 pages)
 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 NewtonLeibniz 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
 Isbn
 9781447168119
 Label
 Lectures on Functional Analysis and the Lebesgue Integral
 Title
 Lectures on Functional Analysis and the Lebesgue Integral
 Statement of responsibility
 by Vilmos Komornik
 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 nontraditional 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, clearcut versions of the classical theorems of FubiniTonelli and RadonNikodým. 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.
 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)
 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 NewtonLeibniz 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
 9781447168119
 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, noncommercial 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
 10.1007/9781447168119
 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)
 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 NewtonLeibniz 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
 9781447168119
 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, noncommercial 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
 10.1007/9781447168119
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/LecturesonFunctionalAnalysisandtheLebesgue/PeNLG2uMLcQ/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/LecturesonFunctionalAnalysisandtheLebesgue/PeNLG2uMLcQ/">Lectures on Functional Analysis and the Lebesgue Integral, by Vilmos Komornik, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>