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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:

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Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Peter Philip
LMU Munich
MR ID: 639375
Reference #


Posted date
2021-09-13 23:17:08
Revised date
2021-10-21 12:53:51
Notes type
   Standard Course Offering
      Real Analysis

Analysis III: Measure and Integration Theory of Several Variables

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.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v3 PDF (1.4M) 10/21/21