Math 623-- Real
Prof. Andrea R. Nahmod
Office: LGRT 1338
Tel : (413) 545 6031
Email: mylastname at math dot umass dot
and Thursdays 11:30 am - 12:45
pm in LGRT 1322.
Book : Real
Analysis - Measure Theory, Integration and Hilbert Spaces
by Elias M. Stein and Rami Shakarchi
Office hours: Wednesdays 1:00pm-2:30pm. Also: By appointment
and virtually via Email.
Princeton Lectures in Analysis, Vol. III (2005)
Princeton University Press
Note. Some early editions of the
book have an Erratum for Theorem 4.2 Chapter 1: which can be found here(click).
This is the first part of a 2-semester introduction to Real
Analysis: Math 623 in the Fall, and in the Spring Math 624 which
part of Vol. IV of Stein&Shakarchi also. The prerequisites
for this class is a working knowledge undergraduate Analysis
(as for example taught in classes like M523H and M524H at UMass
In the Fall semester we will cover the
following material from Stein-Shakarchi's Vol III:
1) Measure theory: Lebesgue measure and Integrable functions
2) Integration theory: Lebesgue integral, convergence theorems and
Fubini theorem (Chapter 2)
3) Differentiation and Integration. Functions of bounded variation
4) Abstract measure theory (first part of Chapter 6)
In this semester we will cover most - though not all - of
chapters 1, 2, 3(part), 6 (part) and some additional
will be a 2 hours exam (in class) on Friday
November 10th starting 6PM (room TBD).
Home Exam (click ). Due
12/15/2017 no later than 11AM.
Grading Policy: Homework + Class Participation(40 %)
-- Midterm (30 %) -- Final (30 %)
Fubini and Product Sets ( end of Section 3 Chapter
2 of Stein&Shakarchi).
3.2 Chapter 3 Section 3.1 (Stein-Shakarchi Vol
1(ii) of Theorem 3.4 Chapter 3 Section 3.1
(Stein-Shakarchi Vol III)
HOMEWORKS : Homework will be posted here in a
cummulative fashion and with specific due dates. No
late homeworks will be accepted -
-except for extraordinary circumstances (please talk to me
the due date in those cases).