# Math 4121 Home Page, Spring 2018

## SYLLABUS AND COURSE INFORMATION

**Instructor:**
Steven G. Krantz

**Course Title:**
The Lebesgue Integral

**Textbook:**
* Elementary Introduction to the Lebesgue Integral * by Steven G. Krantz

In fact the book is right here---yours
for free download:

* Elementary Introduction to the Lebesgue Integral * by Steven G. Krantz

**Office:**
103, Cupples I

**Office Hour:**
MWF 11:00am-noon.

**Phone:** (314) 935-6712

**e-mail:**
sk@math.wustl.edu

**Personal Web Address:**
http://www.math.wustl.edu/~sk

**Class Web Page:**
The class Web page is:

http://www.math.wustl.edu/~sk/math4121.html

You can also just go to my personal Web page (above)
and click on the button

for Math 4121.

**Dept. Office:**
100, Cupples I

**Dept. Phone:**
(314) 935-6760

### Course Description:

The purpose of this course is to learn about the theory of
Lebesgue measure and the Lebesgue integral. This integration theory is
quite different from the Riemann integral which you already know.
The course will be challenging but also quite interesting.

### Prerequisites for the Course:

You should
be familiar with the basic topology of the real line
(open and closed sets), you should be familiar with
Cantor's theory of cardinality (countable and uncountable sets),
and you should be comfortable with proofs. Everything in this
course will be proved.

### Work Required in the Course:

There will be regular homework
assignments. These will be handgraded in the usual manner.
There will also be a midterm exam and a final exam.

## The relative weights of the course components are as follows:

**Homework:**
25%

**Midterm:**
35%

**Final:**
40%

### First Homework Assignment:

Due Wednesday, January 31 in class.

pages 17-19: #1, 3, 5, 6, 8, 9, 11

### Second Homework Assignment:

Due Monday, February 12 in class.

pages 25-26: #1, 2, 4, 5, 6, 8, 9, 11

### Third Homework Assignment:

Due Monday, February 26 in class.

pages 30-31: #1, 2, 4, 5, 7, 8, 10, 11, 12

### Fourth Homework Assignment:

Due Monday, March 19 in class.

pages 40-42: #1, 2, 3, 5, 7, 8, 9, 10, 12

### Fifth Homework Assignment:

Due Monday, April 16 in class.

pages 52-53 (Chapter 5): #1, 3, 6, 9, 13

pages 59-60 (Chapter 6): #2, 6, 9

page 68 (Chapter 7): #1, 4, 6, 8

### Sixth and Last Homework Assignment:

Due Friday, April 27 in class.

pages 79-80, Chapter 8: #2, 3, 6, 7

pages 92-93, Chapter 9: #1, 3, 6, 10

pages 99, Chapter 10: #2, 5, 7