About this book
Introduction
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 selfcontained introduction to the theory of realvalued 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 firstyear graduate students, both as a classroom text and a selfstudy guide.
Reviews of first edition:
The book is a clear and wellstructured 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 upperdivision undergraduate or firstyear 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
Keywords
Bibliographic information
 Book Title Basic Real Analysis

Authors
Houshang H. Sohrab
 DOI https://doi.org/10.1007/9781493918416
 Copyright Information Springer Science+Business Media New York 2014
 Publisher Name Birkhäuser, New York, NY
 eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
 Hardcover ISBN 9781493918409
 Softcover ISBN 9781493937141
 eBook ISBN 9781493918416
 Edition Number 2
 Number of Pages XI, 683
 Number of Illustrations 3 b/w illustrations, 0 illustrations in colour

Topics
Measure and Integration
Mathematical Logic and Foundations
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