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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:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

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.

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

contact


Peter Philip
LMU Munich
MR ID: 639375
Reference #
OMN:202109.111308

Attributes

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