Enrollment: 
For problems with and questions about enrollment please contact Sandra Yates (syates-at-ucsc-edu) at the Math office.

Instructor:
Maria Schonbek
email: schonbek at ucsc dot edu
phone: 459-4657
Office: McHenry 4126
Office Hours: T: 12am -1pm, Th 2pm-3pm

Lectures: T-Th 10::-11:45, McHenry 1270

Textbook: Real and Complex Variables, 3rd edition, Rudin

Grading procedures:
Homework 10 %, Midterm 40 %, Final 50 %
No late homework accepted.

Syllabus
This Syllabus gives a general idea of the progress of the class. There will be variations depending on how fast certain topics are understood.
1. Abstract Integration: measure theory and integration.
2. Riesz representation Theorem.
3. Lebesgue measure.
4. Continuity properties of measurable functions
5. L^p spaces.
6. Complex measures : Radon-Nikodym Theorem and applications.
7. Fundamental Theorem of calculus.
8. Product measures; Fubini Theorem.

First Midterm: February 14
  

Homework problems will be assigned on this webpage each  Friday  and will be due the following Thursday.
(This might be changed.) The homework has to be typed.

Homework problems:

HW1:
Page 31: 1, 2, 3, 5.

A.Let (x,M,m) be a measure space. Let A be a dense set in R. Show that the function f: X into R is measurable if an only if  the set {x in X: f(x) \geq a}
is measurable for all a in A.

B.Give an example of a nonmeasurable function.