**A major revision of an MAA classic and perennial bestseller!**

This is a revised, updated and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications.

The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is thus suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis.

Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: for example, the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series.

This book recaptures the sense of wonder that was associated with the subject in its early days. A must for your mathematics library.

The hardcover version of this book is no longer available. A paperback Print-on-Demand version may be ordered below. Print-on-Demand (POD) books are not returnable because they are printed at your request. Damaged books will, of course, be replaced (customer support information is on your receipt).

* As a textbook, *Primer* does have DRM. Our DRM protected PDFs can be downloaded to **three** computers. Please note that the secure PDFs will open only on the Mac and Windows operating systems. iOS (iPad & iPhone) and Linux are *not* supported at this time. Click here for more information.

Electronic ISBN: 9781614440130

Paperback ISBN: 9780883850442