Modern analysis / Kenneth Kuttler.
"Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and rese...
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| Online Access: |
Full Text (via Taylor & Francis) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
2018.
|
| Series: | CRC revivals.
Studies in advanced mathematics. |
| Subjects: |
MARC
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| 100 | 1 | |a Kuttler, Kenneth, |e author. |0 http://id.loc.gov/authorities/names/n97076290 |1 http://isni.org/isni/0000000034814484. | |
| 245 | 1 | 0 | |a Modern analysis / |c Kenneth Kuttler. |
| 264 | 1 | |a Boca Raton, FL : |b CRC Press, |c 2018. | |
| 264 | 4 | |c ©1998. | |
| 300 | |a 1 online resource (572 pages) | ||
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| 490 | 1 | |a Studies in advanced mathematics. | |
| 490 | 1 | |a CRC revivals. | |
| 504 | |a Includes bibliographical references (pages 561-564) and index. | ||
| 505 | 0 | |a 1. Set Theory and General Topology -- 2. Compactness and Continuous Functions -- 3. Banach Spaces -- 4. Hilbert Spaces -- 5. Calculus in Banach Space -- 6. Locally Convex Topological Vector Spaces -- 7. Measures and Measurable Functions -- 8. The Abstract Lebesgue Integral -- 9. The Construction Of Measures -- 10. Lebesgue Measure -- 11. Product Measure -- 12. The L[superscript p] Spaces -- 13. Representation Theorems -- 14. Fundamental Theorem of Calculus -- 15. General Radon Measures -- 16. Fourier Transforms -- 17. Probability -- 18. Weak Derivatives -- 19. Hausdorff Measures -- 20. The Area Formula -- 21. The Coarea Formula -- 22. Fourier Analysis in R[superscript n] -- 23. Integration for Vector Valued Functions -- 24. Convex Functions -- App. 1. The Hausdorff Maximal theorem -- App. 2. Stone's Theorem and Partitions of Unity -- App. 3. Taylor Series and Analytic Functions -- App. 4. The Brouwer Fixed Point theorem. | |
| 520 | 2 | |a "Modern Analysis provides coverage of real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. This significant study clearly and distinctively presents the teaching and research literature of graduate analysis:Providing a fundamental, modern approach to measure theoryInvestigating advanced material on the Bochner integral, geometric theory, and major theorems in Fourier Analysis Rn, including the theory of singular integrals and Milhin's theorem - material that does not appear in textbooksOffering exceptionally concise and cardinal versions of all the main theorems about characteristic functionsContaining an original examination of sufficient statistics, based on the general theory of Radon measuresWith an ambitious scope, this resource unifies various topics into one volume succinctly and completely. The contents span basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and some major results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation. Modern Analysis provides ample and well-constructed exercises and examples. Introductory topology is included to help the reader understand such items as the Riesz theorem, detailing its proofs and statements. This work will help readers apply measure theory to probability theory, guiding them to understand the theorems rather than merely follow directions."--Provided by publisher. | |
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