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Real Analysis: Measure Theory, - Hardcover, by Stein Elias M.; - Acceptable j
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eBay-Artikelnr.:406172397142
Artikelmerkmale
- Artikelzustand
- Book Title
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces (P
- ISBN
- 9780691113869
Über dieses Produkt
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691113866
ISBN-13
9780691113869
eBay Product ID (ePID)
44475108
Product Key Features
Number of Pages
424 Pages
Language
English
Publication Name
Real Analysis : Measure Theory, Integration, and Hilbert Spaces
Subject
Mathematical Analysis
Publication Year
2005
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
1.3 in
Item Weight
26.5 Oz
Item Length
9.4 in
Item Width
6.1 in
Additional Product Features
Intended Audience
College Audience
LCCN
2004-114065
Reviews
As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty. . . . [I]t certainly must be on the instructor's bookshelf as a first-rate reference book., "This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones." --Fernando Q. Gouva, MAA Review, "This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones." --Fernando Q. Gouvêa, MAA Review, "This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones."-- Fernando Q. Gouvêa, MAA Review, "We are all fortunate that a mathematician with the experience and vision of E.M. Stein, together with his energetic young collaborator R. Shakarchi, has given us this series of four books on analysis."-- Steven George Krantz, Mathematical Reviews, This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones. -- Fernando Q. Gouva, MAA Review, This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones. -- Fernando Q. Gouvêa, MAA Review, This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones. -- Fernando Q. Gouvea, MAA Review, "This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones."-- Fernando Q. Gouva, MAA Review, This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones., "This series is a result of a radical rethinking of how to introduce graduate students to analysis. . . . This volume lives up to the high standard set up by the previous ones."-- Fernando Q. Gouv'a, MAA Review, "As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty. . . . [I]t certainly must be on the instructor's bookshelf as a first-rate reference book."-- William P. Ziemer, SIAM Review, We are all fortunate that a mathematician with the experience and vision of E.M. Stein, together with his energetic young collaborator R. Shakarchi, has given us this series of four books on analysis., "As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty. . . . [I]t certainly must be on the instructor's bookshelf as a first-rate reference book." --William P. Ziemer, SIAM Review, We are all fortunate that a mathematician with the experience and vision of E.M. Stein, together with his energetic young collaborator R. Shakarchi, has given us this series of four books on analysis. -- Steven George Krantz, Mathematical Reviews, As one would expect from these authors, the exposition is, in general, excellent. The explanations are clear and concise with many well-focused examples as well as an abundance of exercises, covering the full range of difficulty. . . . [I]t certainly must be on the instructor's bookshelf as a first-rate reference book. -- William P. Ziemer, SIAM Review, "We are all fortunate that a mathematician with the experience and vision of E.M. Stein, together with his energetic young collaborator R. Shakarchi, has given us this series of four books on analysis." --Steven George Krantz, Mathematical Reviews
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
515/.7
Table Of Content
Foreword vii Introduction xv 1 Fourier series: completion xvi Limits of continuous functions xvi 3 Length of curves xvii 4 Differentiation and integration xviii 5 The problem of measure xviii Chapter 1. Measure Theory 1 1 Preliminaries 1 The exterior measure 10 3 Measurable sets and the Lebesgue measure 16 4 Measurable functions 7 4.1 Definition and basic properties 27 4. Approximation by simple functions or step functions 30 4.3 Littlewood's three principles 33 5* The Brunn-Minkowski inequality 34 6 Exercises 37 7 Problems 46 Chapter 2: Integration Theory 49 1 The Lebesgue integral: basic properties and convergence theorems 49 2Thespace L 1 of integrable functions 68 3 Fubini's theorem 75 3.1 Statement and proof of the theorem 75 3. Applications of Fubini's theorem 80 4* A Fourier inversion formula 86 5 Exercises 89 6 Problems 95 Chapter 3: Differentiation and Integration 98 1 Differentiation of the integral 99 1.1 The Hardy-Littlewood maximal function 100 1. The Lebesgue differentiation theorem 104 Good kernels and approximations to the identity 108 3 Differentiability of functions 114 3.1 Functions of bounded variation 115 3. Absolutely continuous functions 127 3.3 Differentiability of jump functions 131 4 Rectifiable curves and the isoperimetric inequality 134 4.1* Minkowski content of a curve 136 4.2* Isoperimetric inequality 143 5 Exercises 145 6 Problems 152 Chapter 4: Hilbert Spaces: An Introduction 156 1 The Hilbert space L 2 156 Hilbert spaces 161 2.1 Orthogonality 164 2.2 Unitary mappings 168 2.3 Pre-Hilbert spaces 169 3 Fourier series and Fatou's theorem 170 3.1 Fatou's theorem 173 4 Closed subspaces and orthogonal projections 174 5 Linear transformations 180 5.1 Linear functionals and the Riesz representation theorem 181 5. Adjoints 183 5.3 Examples 185 6 Compact operators 188 7 Exercises 193 8 Problems 202 Chapter 5: Hilbert Spaces: Several Examples 207 1 The Fourier transform on L 2 207 The Hardy space of the upper half-plane 13 3 Constant coefficient partial differential equations 221 3.1 Weaksolutions 222 3. The main theorem and key estimate 224 4* The Dirichlet principle 9 4.1 Harmonic functions 234 4. The boundary value problem and Dirichlet's principle 43 5 Exercises 253 6 Problems 259 Chapter 6: Abstract Measure and Integration Theory 262 1 Abstract measure spaces 263 1.1 Exterior measures and Carathegrave;odory's theorem 264 1. Metric exterior measures 266 1.3 The extension theorem 270 Integration on a measure space 273 3 Examples 276 3.1 Product measures and a general Fubini theorem 76 3. Integration formula for polar coordinates 279 3.3 Borel measures on R and the Lebesgue-Stieltjes integral 281 4 Absolute continuity of measures 285 4.1 Signed measures 285 4. Absolute continuity 288 5* Ergodic theorems 292 5.1 Mean ergodic theorem 294 5. Maximal ergodic theorem 296 5.3 Pointwise ergodic theorem 300 5.4 Ergodic measure-preserving transformations 302 6* Appendix: the spectral theorem 306 6.1 Statement of the theorem 306 6. Positive operators 307 6.3 Proof of the theorem 309 6.4 Spectrum 311 7 Exercises 312 8 Problems 319 Chapter 7: Hausdorff Measure and Fractals 323 1 Hausdorff measure 324 Hausdorff dimension 329 2.1 Examples 330 2. Self-similarity 341 3 Space-filling curves 349 3.1 Quartic intervals and dyadic squares 351 3. Dyadic correspondence 353 3.3 Construction of the Peano mapping 355 4* Besicovitch sets and regularity 360 4.1 The Radon transform 363 4. Regularity of sets whend3 370 4.3 Besicovitch sets have dimension 371 4.4 Construction of a Besicovitch set 374 5 Exercises 380 6 Problems 385 Notes and References 389<b
Synopsis
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels., Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:
LC Classification Number
QA300
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- c***m (445)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufWOW!; I cannot believe this 4 Days to Hawaii! ; AAA+++; Excellent Service; Great Pricing; Fast Delivery-Faster Than Expected to Hawaii!; Shipped 04/19, Sat, Received 04/24 Thur to Hawaii using free shipping; USPS Ground Mail, Paperback Book in Good Condition--Better Than Described ; TLC Packaging; Excellent Seller Communication, Sends updates . Highly Recommended!, Thank you very much!The Great Crash, 1929 - Paperback, by J K Galbraith - Acceptable (Nr. 125958575357)
- c***e (34)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufThe textbook was better than described. It looks like brand new! The price was appropriate for the type of textbook that it is. The appearance and quality of the textbook was impeccable. The shipping took about 2 weeks to arrive, but the textbook was well worth the wait. Seller packaged my textbook beautifully which ensured that it arrived unharmed and in perfect condition. Excellent seller! I would purchase more items from this seller in the future!