Advanced Real Analysis

Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis (available separately or together as a Set), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.


Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and forself-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.