MTH 535
Measure and Integration I

Course Information and Syllabus, Fall 2007

Text:Measure Theory and Probability by M. Adams and V. Guillemin, Wadsworth & Brooks, 1996 

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.

Application of Measure and Integration Theory to Fourier Analysis

Application to Some  Problems in Dynamical Systems: Existence Problems and Asymptotic Behavior of Solutions, Ergodic Theory

Computer Requirements

The use of computer algebra systems such as MATHEMATICA, MAPLE, and Scientific Notebook is encouraged.  Some MATHEMATICA and/or MAPLE notebooks will be provided and demonstrated in the class. Some of the problems may need MAPLE or MATHEMATICA to be solved effectively.

Instructor: Dr. M. Kulenovic,
Phone: 44436
Online information: or

Office: Tyler 216
Office hours: MWF 11-12 and by appointment. 

Time: MW 3-4:15
Place: Tyler Hall 106

Useful links:

Measure Theory at Harvard University

Prof. Kaskosz course in Measure Theory