Basic real analysisAnthony W. Knapp
Cornerstones of Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features:
• Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations
• Subsequent chapters develop measure theory, point-set topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces
• Later chapters provide a higher-level view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis
• Throughout the text are problems that develop and illuminate aspects of the theory of probability
• Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problems.