Instructor: Demetrio Labate

• OFFICE:   PGH 694 
• EMAIL ADDRESS:   dlabate@math.uh.edu 
• HOMEPAGE:   http://www.math.uh.edu/~dlabate 

When and Where

• MEETING TIME:   MWF 11-12,
• MEETING PLACE:   C 105 
• OFFICE HOURS:   MW: 1-2; or by appointment 

Course Description:

This is the first semester of a two-semester sequence. The first semester focuses on the basic principles of measure and integration, which is essential in many areas of mathematics including analysis and probability. This semester will be devoted mostly to the following topics: measures, measurable functions, Lebesgue integration, convergence of sequences of functions. Lp spaces. . 

Textbook:

Lebesgue Integration on Euclidean Space (Revised Ed.), by Frank Jones. Publisher: Jones and Bartlett Books in Mathematics, 2000.  

Prerequisites:

An undergraduate real analysis sequence (Math 4331, 4332) or equivalent. A basic knowledge of topology and metric spaces is useful.

Course outline:

• Lebesgue measure
• Measurable functions
• Lebesgue Integration
• Fubini's Theorem
• Lp spaces

HOMEWORK:

• Homework 1: HW1 assignment - [Due: 9/7/2012]  
• Homework 2: HW2 assignment - [Due: 9/21/2012]  
• Homework 3: Ch.2, Problems 25,27,29,31 - [Due: 10/01/2012]  
• Homework 4: Ch.3, Problems 13,15;Ch.4, Problems 8,9; Ch.5, Problem 2. - [Due: 10/17/2012]  
• Homework 5: HW5 assignment - [Due: 10/31/2012]  
• Suggested problems: Ch.6: Prob. 8,12,19,21; Ch.7: Prob. 6,9 - [Not to be collected]  
• Homework 6: HW6 assignment - [Due: 11/16/2012]  
• Homework 7: HW7 assignment - [Due: 12/3/2012]  

Tests and Exam Dates:

The dates for the two midterm exams are (tentatively) Wed Oct 3 and Wed Nov 14.

• Here is the Final Take-Home Exam: Final Exam - [Due: 12/10/2012 - 11AM]  

Grading:

Grades will be based on homework assignments counting 40% towards the final grade, on two midterm exams counting 30% towards the final grade and one final counting 30% towards the final grade. 

The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).