Machine generated contents note: Set Theory The Real Number System and Calculus Lebesgue Measure on the Real Line The Lebesgue Integral on the Real Line Elements of Measure Theory Extensions to Measures and Product Measure Elements of Probability Differentiation and Absolute Continuity Signed and Complex Measures Topologies, Metrics, and Norms Separability and Compactness Complete and Compact Spaces Hilbert Spaces and Banach Spaces Normed Spaces and Locally Convex Spaces Elements of Harmonic Analysis Measurable Dynamical Systems Hausdorff Measure and Fractals .
"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"-- Provided by publisher.