**Graduate Studies in Mathematics**

Volume: 117;
2010;
349 pp;
Hardcover

MSC: Primary 42; 46;

Print ISBN: 978-0-8218-5278-1

Product Code: GSM/117

List Price: $66.00

Individual Member Price: $52.80

**Electronic ISBN: 978-1-4704-1179-4
Product Code: GSM/117.E**

List Price: $66.00

Individual Member Price: $52.80

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#### Supplemental Materials

# An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog

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*Terence Tao*

In 2007 Terry Tao began a mathematical blog to cover a variety of topics, ranging from his own research and other recent developments in mathematics, to lecture notes for his classes, to nontechnical puzzles and expository articles. The first two years of the blog have already been published by the American Mathematical Society. The posts from the third year are being published in two volumes. The present volume consists of a second course in real analysis, together with related material from the blog.

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 Carathéodory 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.

#### Table of Contents

# Table of Contents

## An Epsilon of Room, I: Real Analysis: pages from year three of a mathematical blog

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Real analysis 114 free
- Related articles 275288
- Bibliography 339352
- Index 345358 free
- Back Cover Back Cover1370

#### Readership

Graduate students interested in analysis.

#### Reviews

It is a nice contribution to the current literature by one of the leading mathematicians in the world and can only be warmly recommended to everybody interested in these topics.

-- Monatshafte für Mathematik