Introduction to Real Analysis

  • Christopher Heil

Part of the Graduate Texts in Mathematics book series (GTM, volume 280)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. Christopher Heil
    Pages 15-32
  3. Christopher Heil
    Pages 33-86
  4. Christopher Heil
    Pages 87-118
  5. Christopher Heil
    Pages 119-176
  6. Christopher Heil
    Pages 177-218
  7. Christopher Heil
    Pages 253-288
  8. Christopher Heil
    Pages 289-326
  9. Christopher Heil
    Pages 327-386
  10. Back Matter
    Pages 387-400

About this book


Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject.

The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more.

Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.


Real analysis math Real analysis introduction Real analysis intro textbook Lebesgue measure Lebesgue integration Hilbert spaces Bounded variation Orthonormal bases Fourier transform Fourier series Banach spaces functional analysis operator theory random measures topological vector spaces

Authors and affiliations

  • Christopher Heil
    • 1
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

Bibliographic information