Basic Real Analysis

  • Houshang H. Sohrab

Table of contents

  1. Front Matter
    Pages i-xi
  2. Houshang H. Sohrab
    Pages 1-37
  3. Houshang H. Sohrab
    Pages 39-96
  4. Houshang H. Sohrab
    Pages 97-127
  5. Houshang H. Sohrab
    Pages 129-179
  6. Houshang H. Sohrab
    Pages 181-239
  7. Houshang H. Sohrab
    Pages 241-289
  8. Houshang H. Sohrab
    Pages 291-344
  9. Houshang H. Sohrab
    Pages 345-409
  10. Houshang H. Sohrab
    Pages 411-464
  11. Houshang H. Sohrab
    Pages 465-526
  12. Houshang H. Sohrab
    Pages 527-573
  13. Houshang H. Sohrab
    Pages 575-654
  14. Back Matter
    Pages 655-683

About this book


This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language.

The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus.

With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition, is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide.

Reviews of first edition:

The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis.

—Zentralblatt MATH

The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest.

—Mathematical Reviews

[This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear.

—CHOICE Reviews


Banach and Hilbert Spaces Differential Calculus Fourier Series Lebesgue Integral Lebesgue Measure Measure and Probability Metric Spaces Monotone Functions Normed and Function Spaces Riemann Integral Set Theory

Authors and affiliations

  • Houshang H. Sohrab
    • 1
  1. 1.MathematicsTowson UniversityTowsonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1840-9
  • Online ISBN 978-1-4939-1841-6
  • About this book