Ebook: Basic real analysis

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.