Approved January 31, 2007.
Course Request Summary
Department Submitting Request: Mathematics
Request for Action: CHANGE
Effective: 200703
Course Subject Area: Mathematics
Subject Code: MAT
Course Number: 206
Descriptive Title: Measure Theory
Abbreviated Title: Measure Theory
Units: 4
Learning Activity
1st LEC 3.0 hrs/wk
2nd PRB 0.0 hrs/wk
In Progress Grading: None
Consent of Instructor: No
Prerequisite(s): Course 125B
Restrictions on
Enrollment:
Course Description: Introduction to measure theory. The study of lengths, surface areas, and volumes in general spaces, as related to integration theory.
General Education: No GE Certification
Topical Breadth:
Diversity:
Writing Experience:
Cross Listing: Same Course as
Justification:
Repeat Credit: No
Credit Limitations:
Mode of Grading: Letter
Quarters to be Offered: III Alternate Years
Instructors Name(s): Staff, Chair in Charge Title(s):
Remarks:
Change of prerequisite due to changes in our undergraduate courses and degree requirements. Math 127C is canceled. The material from former 127C will now be in Math 125B.
Expanded Course
Description
TOPICAL OUTLINE:
Measures and outer measures; Lebesgue measure.
Measurable functions and integration; types of convergence; monotone and Lebesgue dominated convergence theorems.
L^p spaces and their completenes.
Product measures and Fubini's theorem.
Differentiation of measures and the Radon-Nikodym theorems.
Measures on locally compact spaces. Radon measures; Riesz representation theorem.
Measure Theory, Donald L. Cohn, Springer, 1996
GRADING PERCENTAGES:
COURSE FORMAT AND REQUIREMENTS:
Student workload is 3 hours of lecture, 6 hours of outside preparation, and 3 hours of extensive problem solving for a total of 12 hours per week.
EXPLANATION OF POTENTIAL COURSE OVERLAP:
None
GENERAL EDUCATION JUSTIFICATION:
None
ADDITIONAL INFORMATION FOR STUDENTS: