Measure and integration
Master
In Maynard (USA)
Description
-
Type
Master
-
Location
Maynard (USA)
-
Start date
Different dates available
This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.
Facilities
Location
Start date
Start date
Reviews
Course programme
Lectures: 2 sessions / week, 1.5 hours / session
This course will be an introduction to abstract measure theory and the Lebesgue integral. We will begin by defining the Lebesgue integral, prove the main convergence theorems, and construct Lebesgue measure in Rn. Other topics include Lp- spaces, Radon-Nikodym Theorem, Lebesgue Differentiation Theorem, Fubini Theorem, Hausdorff measure, and the Area and Coarea Formulas.
Analysis I (18.100)
Rudin, Walter. Real and Complex Analysis. McGraw-Hill International Editions: Mathematics Series. McGraw-Hill Education - Europe, 1986. ISBN: 9780070542341.
Jones, Frank. Lebesgue Integration on Euclidean Space. Boston: Jones & Bartlett Publishers, February 1, 1993.
Evans, Lawrence C., and Ronald F. Gariepy. Measure Theory and Fine Properties of Function. Boca Raton, Florida: CRC Press, December 18, 1991. ISBN: 0849371570.
There will be homework assignments (scheduled to be determined by a stochastic process) and no exams.
The basis for the course grade is class attendance and turning in homework assignments.
Don't show me this again
This is one of over 2,200 courses on OCW. Find materials for this course in the pages linked along the left.
MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.
No enrollment or registration. Freely browse and use OCW materials at your own pace. There's no signup, and no start or end dates.
Knowledge is your reward. Use OCW to guide your own life-long learning, or to teach others. We don't offer credit or certification for using OCW.
Made for sharing. Download files for later. Send to friends and colleagues. Modify, remix, and reuse (just remember to cite OCW as the source.)
Learn more at Get Started with MIT OpenCourseWare
Measure and integration