An Epsilon of Room, I: Real Analysis (Graduate Studies in Mathematics, 117)
Language: English
Published by American Mathematical Society, 2022
- Softcover
- New
Seller: Majestic Books, Hounslow, United KingdomMajestic Books
AbeBooks seller since January 19, 2007
Condition: New
£ 94.93
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- Title
- An Epsilon of Room, I: Real Analysis (Graduate Studies in Mathematics, 117)
- Author
- Terence Tao
- Publisher
- American Mathematical Society
- Publication year
- 2022
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 1470471612
- ISBN 13
- 9781470471613
- Series
- Book 96 of 190: Graduate Studies in Mathematics
The real analysis course assumes some familiarity with general measure theory, as well as fundamental notions from undergraduate analysis. The text then covers more advanced topics in measure theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz representation theorem, topics in functional analysis, such as Hilbert spaces and Banach spaces, and the study of spaces of distributions and key function spaces, including Lebesgue's $L^p$ spaces and Sobolev spaces. There is also a discussion of the general theory of the Fourier transform.
The second part of the book addresses a number of auxiliary topics, such as Zorn's lemma, the Caratheodory extension theorem, and the Banach-Tarski paradox. Tao also discusses the epsilon regularisation argument--a fundamental trick from soft analysis, from which the book gets its title. Taken together, the book presents more than enough material for a second graduate course in real analysis.
The second volume consists of technical and expository articles on a variety of topics and can be read independently.
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Majestic Books
Hounslow, United Kingdom
AbeBooks seller since January 19, 2007
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