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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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An Epsilon of Room, I: Real Analysis - pages from year three of a mathematical blog (Paperback)
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An Epsilon of Room, I: Real Analysis - pages from year three of a mathematical blog (Paperback)
Series: Graduate Studies in Mathematics
Expected to ship within 12 - 17 working days
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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
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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