MARC details
| 000 -LEADER |
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| fixed length control field |
03302nam a22003617a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240508175041.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
240506b |||||||| |||| 00| 0 hin d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783030331429 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
NISER LIBRARY |
| Language of cataloging |
eng |
| Transcribing agency |
NISER LIBRARY |
| 041 ## - LANGUAGE CODE |
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| Language code of text/sound track or separate title |
English |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
517 |
| Item number |
AXL-M |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Axler, Sheldon. |
| 245 ## - TITLE STATEMENT |
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| Title |
Measure, integration and real analysis |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc. |
New York : |
| Name of publisher, distributor, etc. |
Springer, |
| Date of publication, distribution, etc. |
2020. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xviii, 411p. : |
| Other physical details |
illustrations (colour) ; |
| Dimensions |
25 cm. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Graduate texts in mathematics ; |
| Volume/sequential designation |
282 |
| International Standard Serial Number |
0072-5285 |
| 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.<br/><br/>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.<br/><br/>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.<br/><br/>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 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Measure Theory |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Integration, Functional |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical Analysis |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Riemann Integration |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Lebesgue Integration |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Lebesgue Differentiation Theorem |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Banach Spaces |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Hilbert Spaces |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Riesz Representation Theorem |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Table of contents |
| Uniform Resource Identifier |
<a href="https://link.springer.com/book/10.1007/978-3-030-33143-6#toc">https://link.springer.com/book/10.1007/978-3-030-33143-6#toc</a> |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Reviews |
| Uniform Resource Identifier |
<a href="https://www.goodreads.com/book/show/51019857-measure-integration-real-analysis?from_search=true&from_srp=true&qid=9ZzDJkqdUz&rank=1#CommunityReviews">https://www.goodreads.com/book/show/51019857-measure-integration-real-analysis?from_search=true&from_srp=true&qid=9ZzDJkqdUz&rank=1#CommunityReviews</a> |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Electronic version |
| Uniform Resource Identifier |
<a href="https://link.springer.com/book/10.1007/978-3-030-33143-6#bibliographic-information">https://link.springer.com/book/10.1007/978-3-030-33143-6#bibliographic-information</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Koha item type |
Book |
| Source of classification or shelving scheme |
Universal Decimal Classification |
