18.125 | Fall 2003 | Graduate

Measure and Integration


Course Meeting Times

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 Lpspaces, Radon-Nikodym Theorem, Lebesgue Differentiation Theorem, Fubini Theorem, Hausdorff measure, and the Area and Coarea Formulas.


Analysis I (18.100)


Required Text

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.

Examinations and Homework

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.

Course Info

As Taught In
Fall 2003
Learning Resource Types
Lecture Notes
Problem Sets