Overview
The second edition includes three expanded chapters, additional problems, and an application to fixed-point theory
New solutions manual available to instructors upon request
Elegant proofs and excellent choice of topics
Numerous examples and exercises to enforce methodology; exercises integrated into the main text, as well as at the end of each chapter
Special topics on Banach and Hilbert spaces and Fourier series, often not included in many courses on real analysis
Solid preparation for deeper study of functional analysis
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
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
Authors and Affiliations
About the author
Houshang H. Sohrab is a Professor of Mathematics at Towson University.
Bibliographic Information
Book Title: Basic Real Analysis
Authors: Houshang H. Sohrab
DOI: https://doi.org/10.1007/978-1-4939-1841-6
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2014
Hardcover ISBN: 978-1-4939-1840-9Published: 15 November 2014
Softcover ISBN: 978-1-4939-3714-1Published: 15 November 2014
eBook ISBN: 978-1-4939-1841-6Published: 15 November 2014
Edition Number: 2
Number of Pages: XI, 683
Number of Illustrations: 3 b/w illustrations
Topics: Measure and Integration, Mathematical Logic and Foundations