Real Analysis: Measure Theory, Integration, and Hilbert Spaces Elias M. Stein and Rami Shakarchi is an English-language textbook focused on the core areas of analysis. The book covers in depth topics such as measure and integration theory, differentiation, Hilbert spaces, and fractal geometry.
This third volume in the Princeton Lectures in Analysis series offers an integrated approach to real analysis, highlighting the organic interconnections between the different parts of analysis. After a clear exposition of measure theory and Lebesgue integration, the theory of Hilbert spaces via L2 spaces is introduced.
Practical applications of the theories in Fourier analysis, partial differential equations, and complex analysis are developed. In addition, the book introduces fractal structures, including Hausdorff measure and space-filling curves. Each chapter contains a set of exercises of various levels, with pointers for further study.
This textbook is suitable for students and professionals in mathematics and related fields, such as physics, engineering, and finance.