Text: Measure Theory and Probability by M. Adams and V. Guillemin, Wadsworth & Brooks, 1996
Royden, Real Analysis, 3rd ed. Prentice-Hall, 1988.
R. Wheeden and T. Zygmund, Measure and Integral: An Introduction to Real Analysis, CRC 1977
Prerequisites: Graduate standing, exposure to advanced calculus and basic course in probability
Exams and Grading:
Course grade will be determined based on homework and mid-term and final exams:
Homework: 50 %
Exams: 50 %
The exams will be of the take home variety.
The topics that will be covered are:
Basic Construction of Lebesgue Measure. Lebesgue Integrals. Convergence in measure. Various Limiting Theorems.
Application of Measure and Integration Theory to Probability Theory: Random Variables and Expectations. Laws of Large Numbers.
The use of computer algebra systems such as MATHEMATICA,
and Scientific Notebook is encouraged. Some of the problems may need MAPLE or MATHEMATICA to be solved effectively.
Instructor: Dr. M. Kulenovic,
Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm
Office: Tyler 216/ Lippit 200
Office hours: MW 1-2, F 10-11 and by appointment.
Time: MW 3-4:15
Place: Tyler Hall 106
Measure Theory at Harvard University
Kaskosz course in Measure Theory