**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.

#### Readership

Graduate students interested in analysis.

#### Reviews & Endorsements

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

#### 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