Real Analysis I : Math 623
Meeting : TuTh 9:3010:45 LGRT 1234
Instructor : Luc ReyBellet
Office : 1423 J LGRT
Phone : 5456020
EMail : luc@math.umass.edu
Office Hours :
M 1:302:30, Tu 2:004:00pm, Th 11:3012:30 , or by appointment.
Text: The text book for the class is

Real Analysis. Measure Theory, Integration & Hilbert Spaces,
by E. M. Stein & R. Shakarchi. Princeton Lecture Notes in Analysis III, Princeton University
Press 2005.
Erratum: Correct proof of Theorem 4.2, Chapter 1
SUP#2 PDF file
Other very useful references:

Real Analysis: Modern Techniques and their applications,
by G.B. Folland. 2nd ed. Wiley 1999.

Real Analysis, by H.L. Royden. 3rd ed. Collier Macmillan 1988

Measure and Integral: An Introduction to Real Analysis,
by R.L. Wheeden and A. Zygmund. M Dekker 1977.

A Radical Approach to Lebesgue's Theory of Integration,
by D. M. Bressound. (MAA textbooks) Cambridge University Press 2008.
My alltime favourite undegraduate analysis text:

Analysis by its History,
by E. Hairer and G. Wanner. Undergraduate Texts in Mathematics. Springer
Syllabus:
This is the first part of a 2semester introduction to real analysis
(Math 623624). The prerequisites for this class is a working knowledge of
the basics of analysis taught in a class like M523, see for example Chapter 3
and 4 of Analysis by its History.

1) Measure theory: Lebesgue measure and Integrable functions

2) Integration theory: Lebesgue integral, convergence theorems and Fubini theorem

3) Differentiation and Integration. Functions of bounded variation.

4) Hilbert spaces and Banach spaces . Examples and Applications. Inequalities.

5) Abstract measure theory.
Grade: There will be a midterm and a final.
Homework will be assigned regularly.
Exams:
 Midterm: Room:
 Final: Room:
Homework :
Homework #1 (due on September 28):
Set #1
Homework #2 (due on October 19 ):
Set #2
Homework #3 (due on November 9):
Set #3
Homework #4 (due on November 30 ):
Set #4
Homework #5 (due on December 13 ):
Set #5