Softcover ISBN:  9781470471613 
Product Code:  GSM/117.S 
List Price:  $70.00 
MAA Member Price:  $63.00 
AMS Member Price:  $56.00 
Electronic ISBN:  9781470411794 
Product Code:  GSM/117.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 

Book DetailsGraduate Studies in MathematicsVolume: 117; 2010; 349 ppMSC: Primary 42; 46;
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 LebesgueRadonNikodym 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 BanachTarski 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.ReadershipGraduate students interested in analysis.

Table of Contents

Chapters

Chapter 1. Real analysis

Chapter 2. Related articles


Additional Material

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


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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 LebesgueRadonNikodym 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 BanachTarski 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.
Graduate students interested in analysis.

Chapters

Chapter 1. Real analysis

Chapter 2. Related articles

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