Modern analysis /
"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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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
2018.
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| Series: | Studies in advanced mathematics
CRC revivals |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | "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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| Physical Description: | 1 online resource (572 pages) |
| ISBN: | 9780203711316 0203711319 9781351360005 1351360000 1351359991 9781351359993 9781351359986 1351359983 |