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)
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.