Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:
Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.
3rd part of 3-semester course on Calculus and Real Analysis: A detailed introduction to abstract measure theory is followed by the study of abstract integration of real- and complex-valued measurable maps. Noteworthy theorems include dominated convergence, Fubini, and change of variables. L^p spaces are studied, including an introduction to convolution and Fourier transform. An introductory section on the integration over submanifolds of R^n culminates in the Gauss-Green Theorem.