Basic Real Analysis

Cornerstones, Birkhäuser, Boston, 2005.
ISBN: 0-8176-3250-6 for the single volume.
653+xxii pages.

ISBN: 0-8176-4407-5 for the two-volume set with Advanced Real Analysis.

There is now a  Digital Second Edition of this book.  It is available only in electronic form.

Chapter Titles: 

Theory of Calculus in One Real Variable
Metric Spaces
Theory of Calculus in Several Real Variables
Theory of Ordinary Differential Equations and Systems
Lebesgue Measure and Abstract Measure Theory
Measure Theory for Euclidean Space
Differentiation of Lebesgue Integrals on the Line
Fourier Transform in Euclidean Space
L^p Spaces
Topological Spaces
Integration on Locally Compact Spaces
Hilbert and Banach Spaces

File Available:

Front matter - PDF


The final list of corrections to the 2005 version appears in the file below.  Many of these corrections were kindly sent to the author either by S. H. Kim of South Korea or by Jacques Larochelle of Canada. The correction on pages 39 and 40 was kindly sent by Glenn Jia of China. The long correction for pages 596-598 resulted from a discussion with Qiu Ruyue.

Corrections (2/15/2015) - PDF

Last modified: 1/27/2016