MATH 70200: Functions of a Real Variable II

Spring 2014

Description: This is the second part of a year-long course in classical real analysis. It covers abstract Lebesgue integration, measure and topology, $L^p$ spaces, differentiation of measures and functions, as well as elementary theory of Banach and Hilbert spaces. The course assumes a good knowledge of the topics covered in Math 70100. Left: A Cantor set embedded in 3-dimensional space

Lecturer: Saeed Zakeri
Office: Room 4301, Tel: (212) 817-8559
Office Hours: By appointment
Class meetings: Wednesday and Friday 12:00-1:30PM, Room 5417
email: saeed DOT zakeri AT qc DOT cuny DOT edu

Syllabus

References

Homework

Announcements:

• 6/3: Check out final exam solutions. I'll post your grades in a couple of days.

• 5/22: Check out the take-home final exam.

• 4/8: The results of the midterm exam are given by the grade vector $(60,57,53,49,44,42,40,20) \in {\mathbb R}^8$. I'll return the tests tomorrow.

• 4/2: Check out midterm exam solutions.

• 3/30: Check out the take-home midterm exam.

• 3/22: Following up on a question raised during lecture, it turns out that Sierpinski indeed constructs a non-measurable subset of the unit square that meets every horizontal or vertical segment at most once. The proof uses transfinite induction to carefully pick one point from each compact subset of positive measure of the square. See
  W. Sierpinski, Sur un probl`eme concernant les ensembles mesurables superficiellement. Fund. Math. 1920. V. 1. P. 112–115.

• 2/8: A reminder that there will be no class on Wednesday 2/12 (Lincoln's birthday). We will resume lecture on Friday 2/14.

• 1/31: Welcome!

General Information:

• Homework will be assigned roughly every week and is an absolutely essential part of the course. You are strongly advised to work on all the homework problems to make sure you are keeping pace with the class. You are also encouraged to work together on these problems, but the work that you hand in must be your own write up.

• Course grade is based on the following scheme:
  
  

  Homework	Midterm	Final
  20%	30%	50%

• Exams are scheduled as follows:
  
  

  Midterm	Final
  Wednesday April 2	TBA

• If the midterm exam is missed because of a documented illness or valid emergency, the course grade will be determined on the basis of the other work done during the semester. Exams missed for other reasons will count as failures.

• At the end of the semester, everyone who has not withdrawn from the class will receive a grade. Incompletes will not be given to avoid unsatisfactory grades.