Coverart for item
The Resource Measure, Integration & Real Analysis, by Sheldon Axler, (electronic resource)

Measure, Integration & Real Analysis, by Sheldon Axler, (electronic resource)

Label
Measure, Integration & Real Analysis
Title
Measure, Integration & Real Analysis
Statement of responsibility
by Sheldon Axler
Creator
Subject
Language
eng
Summary
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Axler, Sheldon
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Open Access e-Books
  • Graduate Texts in Mathematics,
Series volume
282
http://library.link/vocab/subjectName
Measure theory
Label
Measure, Integration & Real Analysis, by Sheldon Axler, (electronic resource)
Link
https://doi.org/10.1007/978-3-030-33143-6
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
About the Author -- Preface for Students -- Preface for Instructors -- Acknowledgments -- 1. Riemann Integration -- 2. Measures -- 3. Integration -- 4. Differentiation -- 5. Product Measures -- 6. Banach Spaces -- 7. L^p Spaces -- 8. Hilbert Spaces -- 9. Real and Complex Measures -- 10. Linear Maps on Hilbert Spaces -- 11. Fourier Analysis -- 12. Probability Measures -- Photo Credits -- Bibliography -- Notation Index -- Index -- Colophon: Notes on Typesetting
Control code
978-3-030-33143-6
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (XVIII, 411 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
  • Open Access
  • 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
9783030331436
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
41 illustrations, 20 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1129397508
Label
Measure, Integration & Real Analysis, by Sheldon Axler, (electronic resource)
Link
https://doi.org/10.1007/978-3-030-33143-6
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
About the Author -- Preface for Students -- Preface for Instructors -- Acknowledgments -- 1. Riemann Integration -- 2. Measures -- 3. Integration -- 4. Differentiation -- 5. Product Measures -- 6. Banach Spaces -- 7. L^p Spaces -- 8. Hilbert Spaces -- 9. Real and Complex Measures -- 10. Linear Maps on Hilbert Spaces -- 11. Fourier Analysis -- 12. Probability Measures -- Photo Credits -- Bibliography -- Notation Index -- Index -- Colophon: Notes on Typesetting
Control code
978-3-030-33143-6
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (XVIII, 411 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
  • Open Access
  • 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
9783030331436
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
41 illustrations, 20 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1129397508

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