MTH 536
Measure and Integration II

Course Information and Syllabus, Spring 2008

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, MTH 535

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:

L1 and L theory, Geometry of Hilbert spaces

Application of Measure and Integration Theory to Probability Theory: Central Limit Theorem

Application of Measure and Integration Theory to Fourier Analysis: Fourier series

Application to Fractal Geometry : Hausdorff Measure and Dimension, IFS 

Application to Ergodic Theory: Invariant Measures, Birkhoff Ergodic Theorem

Application to Some  Problems in Ordinary Differential Equations: Existence Problems and Asymptotic Behavior of Solutions

Computer Requirements

The use of computer algebra systems such as MATHEMATICA, MAPLE 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.

Here is a sample of images that can be easily produced by the software that will be used in this course. See also Dynamica.

Useful links:

Measure Theory at Harvard University

S. Zakeri collection of solved problems

Instructor: Dr. M. Kulenovic,
Phone: 874-4436
Online information: or

Office: Tyler 216
Office hours: MTW 1-2 and by appointment. 

Time: MW 3-4:15