Real analysis
Real analysis
About this book
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
Details
- OL Work ID
- OL23226227W
Subjects
Mathematical analysisTextbooksReal functions -- Instructional exposition (textbooks, tutorial papers, etc.).Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.).Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.).Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.).Special functions (33-XX deals with the properties of functions as functions) -- Instructional exposition (textbooks, tutorial papers, etc.).Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.).Approximations and expansions -- Instructional exposition (textbooks, tutorial papers, etc.).Convex and discrete geometry -- Instructional exposition (textbooks, tutorial papers, etc.).General topology -- Instructional exposition (textbooks, tutorial papers, etc.).Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.).