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Real Analysis--With an Introduction to Wavelet Theory
Satoru Igari, Tohoku University, Sendai, Japan

Translations of Mathematical Monographs
1998; 256 pp; softcover
Volume: 177
Reprint/Revision History:
reprinted 2000
ISBN-10: 0-8218-2104-0
ISBN-13: 978-0-8218-2104-6
List Price: US$95
Member Price: US$76
Order Code: MMONO/177.S
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This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and wavelet theory.


  • The core subjects of real analysis.
  • The fundamentals for students who are interested in harmonic analysis, probability or partial differential equations.

This volume would be a suitable textbook for an advanced undergraduate or first year graduate course in analysis.


Advanced undergraduates and graduate students studying real analysis; physicists, engineers.


"The presentation is clear and rigorous."

-- SIAM Review

"The author has done a fine job in presenting the material selected for this book. The reader is exposed to a variety of real analysis concepts, methods, and techniques. The value of Igari's book lies in this exposition; it combines, contrasts, and reveals those concepts that are vital for a future deeper study of real analysis and its applications. The presentation of the material is clear and precise; well-chosen examples and exercises help the student to master the subject matter at hand ... highly recommend this textbook to anyone who is interested in learning about the fundamentals of real and functional analysis, distribution and Fourier theory, and their applications to wavelet theory."

-- Mathematical Reviews

"The book is a nice and compact introduction to Real Analysis. The material has been selected with a good taste and presented in a clear form. Each chapter is supplied with a list of problems, the solutions to which are presented at the end of the book. The bibliography reflects recent developments and contains the titles of the best books in the area."

-- Zentralblatt MATH

Table of Contents

  • Euclidean spaces and the Riemann integral
  • Lebesgue measure on Euclidean spaces
  • The Lebesgue integral on Euclidean spaces
  • Differentiation
  • Measures in abstract spaces
  • Lebesgue spaces and continuous functions
  • Schwartz space and distributions
  • Fourier analysis
  • Wavelet analysis
  • Appendix A
  • Appendix B
  • Solutions to problems
  • Bibliography
  • Index
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