The Resource Real Analysis, by Peter A Loeb, (electronic resource)
Real Analysis, by Peter A Loeb, (electronic resource)
Resource Information
The item Real Analysis, by Peter A Loeb, (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 Real Analysis, by Peter A Loeb, (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 is designed for a yearlong course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.
 Language
 eng
 Extent
 1 online resource (xii, 274 pages)
 Contents

 Preface
 Set Theory and Numbers
 Measure on the Real Line
 Measurable Functions
 Integration
 Differentiation and Integration
 General Measure Spaces
 Introduction to Metric and Normed Spaces
 Hilbert Spaces
 Topological Spaces
 Measure Construction
 Banach Spaces
 Appendices
 References
 Isbn
 9783319307442
 Label
 Real Analysis
 Title
 Real Analysis
 Statement of responsibility
 by Peter A Loeb
 Language
 eng
 Summary
 This textbook is designed for a yearlong course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Loeb, Peter A
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/subjectName

 Mathematics
 Functional analysis
 Measure theory
 Functions of real variables
 Label
 Real Analysis, by Peter A Loeb, (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
 Preface  Set Theory and Numbers  Measure on the Real Line  Measurable Functions  Integration  Differentiation and Integration  General Measure Spaces  Introduction to Metric and Normed Spaces  Hilbert Spaces  Topological Spaces  Measure Construction  Banach Spaces  Appendices  References
 Control code
 9783319307442
 Dimensions
 unknown
 Extent
 1 online resource (xii, 274 pages)
 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, 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
 9783319307442
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319307442
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)949407231
 Label
 Real Analysis, by Peter A Loeb, (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
 Preface  Set Theory and Numbers  Measure on the Real Line  Measurable Functions  Integration  Differentiation and Integration  General Measure Spaces  Introduction to Metric and Normed Spaces  Hilbert Spaces  Topological Spaces  Measure Construction  Banach Spaces  Appendices  References
 Control code
 9783319307442
 Dimensions
 unknown
 Extent
 1 online resource (xii, 274 pages)
 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, 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
 9783319307442
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319307442
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)949407231
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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/RealAnalysisbyPeterALoebelectronic/MQsi5_wrto/" 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/RealAnalysisbyPeterALoebelectronic/MQsi5_wrto/">Real Analysis, by Peter A Loeb, (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>