Measure and Integration

Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Description

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

Prerequisite

Analysis I (18.100)

Textbooks

Required Text

Rudin, Walter. Real and Complex Analysis. McGraw-Hill International Editions: Mathematics Series. McGraw-Hill Education - Europe, 1986. ISBN: 9780070542341.

Recommended Additional Texts

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.

Grading

The basis for the course grade is class attendance and turning in homework assignments.