**AMS Chelsea Publishing**

Volume: 376;
2015;
575 pp;
Hardcover

MSC: Primary 26; 28;

**Print ISBN: 978-1-4704-2544-9
Product Code: CHEL/376.H**

List Price: $53.00

AMS Member Price: $47.70

MAA Member Price: $47.70

**Electronic ISBN: 978-1-4704-2725-2
Product Code: CHEL/376.H.E**

List Price: $50.00

AMS Member Price: $45.00

MAA Member Price: $45.00

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#### Supplemental Materials

# An Introduction to Classical Real Analysis

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*Karl R. Stromberg*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

This classic book is a text for a standard introductory course in
real analysis, covering sequences and series, limits and continuity,
differentiation, elementary transcendental functions, integration,
infinite series and products, and trigonometric series. The author has
scrupulously avoided any presumption at all that the reader has any
knowledge of mathematical concepts until they are formally presented
in the book.

One significant way in which this book differs from other texts at
this level is that the integral which is first mentioned is the
Lebesgue integral on the real line. There are at least three good
reasons for doing this. First, this approach is no more difficult to
understand than is the traditional theory of the Riemann
integral. Second, the readers will profit from acquiring a thorough
understanding of Lebesgue integration on Euclidean spaces before they
enter into a study of abstract measure theory. Third, this is the
integral that is most useful to current applied mathematicians and
theoretical scientists, and is essential for any serious work with
trigonometric series.

The exercise sets are a particularly attractive feature of this
book. A great many of the exercises are projects of many parts which,
when completed in the order given, lead the student by easy stages to
important and interesting results. Many of the exercises are supplied
with copious hints. Thanks to the generous help of the author's
friend,
Professor Robert Burckel, this new printing contains a large number of
corrections, a short author biography as well as a list of selected
publications of the author.

Stromberg's book gives an excellent treatment of real analysis. Making no assumption that the reader is familiar with "baby real variables," it starts from the beginning and develops the Lebesgue theory of measure and integration, then applies the techniques to a study of Fourier analysis. The book is a classic, suitable as a text for the standard graduate course. It's great to have it available again!

—Peter Duren, University of Michigan

… it is a splendid book well worth reprinting.

—Tom Körner, University of Cambridge

#### Readership

Undergraduate and graduate students interested in real analysis.

#### Table of Contents

# Table of Contents

## An Introduction to Classical Real Analysis

- Cover Cover11
- Title page iii4
- Contents v6
- Preface xi12
- About the author xiii14
- Preliminaries 116
- Numbers 722
- Sequences and series 3954
- Limits and continuity 91106
- Differentiation 170185
- The elementary transcendental functions 226241
- Integration 257272
- Infinite series and infinite products 398413
- Trigonometric series 502517
- Bibliography 567582
- Other works by the author 569584
- Index 571586
- Back Cover Back Cover1594