Basic Real Analysis

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

[Thistext] 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

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 Request lecturer material: sn.pub/lecturer-material

Autorentext

Houshang H. Sohrab is a Professor of Mathematics at Towson University.

Inhalt

Preface.- Set Theory.- Sequences and Series of Real Numbers.- Limits of Functions.- Topology of R and Continuity.- Metric Spaces.- The Derivative.- The Riemann Integral.- Sequences and Series of Functions.- Normed and Function Spaces.- The Lebesgue Integral.- Lebesgue Measure.- General Measure and Probability.- Appendix A: Construction of Real Numbers.- References.- Index.