A Course in Real Analysis

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

New chapter on Hausdorff Measure and FractalsKey concepts and learning objectives give students a deeper understanding of the material to enhance learningMore than 200 examples (not including parts) are used to illustrate definitions and resultsOver 1300 exercises (not including parts) are provided to promote understandingEach chapter begins with a brief biography of a famous mathematician

1. Set Theory 2. The Real Number System and Calculus 3. Lebesgue Measure on the Real Line 4. The Lebesgue Integral on the Real Line 5. Elements of Measure Theory 6. Extensions to Measures and Product Measure 7. Elements of Probability 8. Differentiation and Absolute Continuity 9. Signed and Complex Measures 10. Topologies, Metrics, and Norms 11. Separability and Compactness 12. Complete and Compact Spaces 13. Hilbert Spaces and Banach Spaces 14. Normed Spaces and Locally Convex Spaces 15. Elements of Harmonic Analysis 16. Measurable Dynamical Systems 17. Hausdorff Measure and Fractals