[内容简介]

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 Fractals
• Key concepts and learning objectives give studentsa deeper understanding of the material to enhance learning
• More than 200 examples (not including parts) are used to illustrate definitions and results
• Over 1300 exercises (not including parts) are provided to promote understanding
• Each chapter begins with a brief biography of a famous mathematician
[目录]
Pt. 1   Set Theory, Real Numbers, and Calculus
1.       Set Theory
          Biography: Georg Cantor
2.       The Real Number System and Calculus
          Biography: Georg Friedrich Bernhard Riemann
Pt. 2   Measure, Integration, and Differentiation
3.       Lebesgue Theory on the Real Line
          Biography: Emile Felix-Edouard-Justin Bore
4.       Measure Theory
          Biography: Henri Leon Lebesgue
5.       Elements of Probability
          Biography: Andrei Nikolaevich Kolmogorov
6.       Differentiation
          Biography: Johann Rado
Pt. 3  Topological, Metric, and Normed Spaces
7.       Elements of Topological, Metric, and Normed Spaces
          Biography: Pavel Samuilovich Urysohn
8.       Complete Spaces, Compact Spaces, and Approximation
          Biography: Marshall Harvey Stone
9.       Hilbert Spaces and the Classical Banach Spaces
          Biography: David Hilbert
10.     Basic Theory of Normed and Locally Convex Spaces
          Biography: Stefan Banach
Pt. 4  Harmonic Analysis and Dynamical Systems
11.    Elements of Harmonic Analysis
         Biography: Ingrid Daubechies
12.    Measurable Dynamical Systems
         Biography: Claude Elwood Shannon