**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

e-mail: kulenm@math.uri.edu
**Online information**: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm

**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