عنوان

Basic real analysis /

(Number (ISBN

1493918419

(Number (ISBN

9781493918416

Erroneous ISBN

1493918400 (print)

Erroneous ISBN

9781493918409

Erroneous ISBN

9781493918409 (print)

Number

dltt

Title Proper

Basic real analysis /

General Material Designation

[Book]

First Statement of Responsibility

Houshang H. Sohrab

Edition Statement

Second edition

Edition Statement

Second edition

Specific Material Designation and Extent of Item

1 online resource (xi, 683 pages)

Text of Note

Includes bibliographical references and index

Text of Note

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

0

Text of Note

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

International Standard Book Number

9781493918409

Mathematical analysis.

QA

Number

Edition

Class number

Sohrab, Houshang H.

Ohio Library and Information Network.

Date of Transaction

20201222075437.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

270410

Y