#
Math 623-- Real
Analysis I

#
Fall 2017

##
Prof. Andrea R. Nahmod

**Office**__:__ **LGRT 1338 **

__Tel __: (413) 545 6031

**Email**__:__ mylastname at math dot umass dot
edu

__Class Meeting__:
Tuesdays
and Thursdays 11:30 am - 12:45
pm in LGRT 1322.

**Office hours**: **Wednesdays 1:00pm-2:30pm. Also: By appointment
and **__virtually via Email.__

__Book__ : *Real
Analysis - Measure Theory, Integration and Hilbert Spaces*
by Elias M. Stein and Rami Shakarchi

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).

__Topics:__
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
covers

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
Amherst).

In the Fall semester we will cover the
following material from Stein-Shakarchi's Vol III:

1) Measure theory: Lebesgue measure and Integrable functions
(Chapter 1)

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

3) Differentiation and Integration. Functions of bounded variation
(Chapter 3)

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
relevant topics.

__Announcements:__

__Midterm
Exam__: *This
will be **an evening 2 hours exam --in class--
on a date TBD*

__Final
Exam____:__* This will be a Take
Home Exam given after the last class and due *__Friday
12/15/2017 no later than 11AM.__

###

Grading Policy:* * Homework + Class Participation(40 %)
-- Midterm (30 %) -- Final (30 %)

__Handouts:__

**Ordering&Zorn
Notes **

Egorov's
Theorem

**On
Fubini and Product Sets ( end of Section 3 Chapter
2 of Stein&Shakarchi).**

**Good
Kernels in Fourier Series (periodic functions)
(from Stein-Shakarchi's ***Fourier Analysis *Volume
I)

**Good
Kernels and Convergence in L^1**

**Lemma
3.2 Chapter 3 Section 3.1 (Stein-Shakarchi Vol
III)**

**Part
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
**before**
the due date in those cases).

**HOMEWORK
SETS (click) **