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

Recommended reading:

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.

**Computer Requirements**

The use of computer algebra systems such as *MATHEMATICA*,
*MAPLE*,
and *Scientific Notebook* is encouraged. Some of the problems may need *MAPLE* or *MATHEMATICA* to be solved effectively.

**Instructor**: Dr. M. Kulenovic,

Phone: 44436

e-mail: *mkulenovic@mail.uri.edu*
**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

**Useful links**:

Measure Theory at Harvard University

Prof.
Kaskosz course in Measure Theory