MARC details
| 000 -LEADER |
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| fixed length control field |
03321nam a2200241 a 4500 |
| 001 - CONTROL NUMBER |
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| control field |
38780 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
0000000000 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240411192908.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
201110n s 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
978-3-030-33142-9 |
| 022 ## - INTERNATIONAL STANDARD SERIAL NUMBER |
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| International Standard Serial Number |
0072-5285 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Axler, Sheldon Jay. |
| 245 10 - TITLE STATEMENT |
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| Title |
Measure, integration & real analysis |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
Sheldon Jay Axler. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Cham : |
| Name of publisher, distributor, etc. |
Springer Open, |
| Date of publication, distribution, etc. |
2020. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource. |
| 500 ## - GENERAL NOTE |
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| General note |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Integral calculus & equations. |
| Source of heading or term |
sears |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Numerical analysis. |
| Source of heading or term |
sears |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://drive.google.com/file/d/1O-YBsFEhMBexQCD-nLauOTmB4_gYHZvF/view?usp=sharing">https://drive.google.com/file/d/1O-YBsFEhMBexQCD-nLauOTmB4_gYHZvF/view?usp=sharing</a> |
