Introduction to Real Analysis

Christopher Heil is Professor of Mathematics at the Georgia Institute of Technology in Atlanta, Georgia. His research interests include harmonic analysis, time-frequency analysis, image processing, and more.

“This book is written in a clear style that is suitable for students reading on their own or as part of a guided class. … this book gives an accessible introduction to real analysis with emphasis on Lebesgue measure and Lebesgue integration in Euclidean spaces. This book could be suitable as a primary text for a first course focused on measure theory in Euclidean spaces or, due to the numerous exercises throughout, as a supplemental text for instructors giving other introductory measure theory courses.” (Gareth Speight, Mathematical Reviews, June, 2020)“This book is intended primarily for students beginning their graduate studies in mathematics but it will also be suitable for well-prepared undergraduates.” (Frédéric Morneau-Guérin, MAA Reviews, February 16, 2020)“The book isreally a textbook full of intermediate motivated questions addressed to the audience and step-divided discussions. It can be suitable for first-year students in mathematics, for well-prepared undergraduate mathematical majors, and for graduate students from a variety of engineering and scientific applications.” (Sergei V. Rogosin, zbMATH 1426.26001, 2020)

• Preliminaries.- 1. Metric and Normed Spaces.- 2. Lebesgue Measure.- 3. Measurable Functions.- 4. The Lebesgue Integral.- 5. Differentiation.- 6. Absolute Continuity and the Fundamental Theorem of Calculus.- 7. The Lp Spaces.- 8. Hilbert Spaces and L^2(E).- 9. Convolution and the Fourier Transform.