Real Analysis: Math 209C
Spring 2004, TTh 8:109:30 in Surge 268
Announcements
 The exam has been graded; let me know if you have not received your grade by email.
Homework
 Homework 6, due May 27.
 Chapter 12: 52, 55 (note: has misprints).
 Chapter 13: 5, 6, 13.
 Homework 5, due May 20.
 Chapter 12: 19, 24, 30, 36, 37, 38.
 Homework 4, due May 13.
 Chapter 12: 1, 10, 13, 17, 21.
 The midterm has been graded.
 Homework 3, due April 29.
 Chapter 7: 47, 48 (take X=R), 50.
 Chapter 9: 42, 43, 44, 46.
 Homework 2, due April 22.
 Chapter 10: 2, 13, 14, 17, 22, 23.
 Homework 1, due April 15.
 Chapter 7: 31, 34, 35, 36, 38.
 Chapter 10: 7, 26, 29.
Syllabus
Professor: Michael Anshelevich, 250 Surge Building.
Office hours: TTh 9:3010:30 am, W 910 am.
Text: H.L.Royden, "Real Analysis," 3rd edition, PrenticeHall, 1988.
Prerequisites: Math 209AB.
Topics:

Operators in Banach spaces. Three basic principles of functional analysis (Chapter 10, sections 14, also 7.8).

Two theorems about function spaces: ArzelaAskoli, StoneWeierstrass (7.10, 9.9).

Outer measures. Extension of measures. Caratheodory construction (Chapter 12).

Product measures. Fubini theorem (Chapter 12).

Time permitting: measures as functionals. Riesz representation theorem (Chapters 12, 13).
Exams: We will have a takehome midterm handed out April 29, due May 6. The final exam is on Monday, June 7, 3:006:00 pm. No makeup exams will be given. If you miss the final, you automatically fail the course. On the takehome exam, books and notes are allowed, collaboration is not. The final is closed book, closed notes.
Homework: weekly, due Thursdays in class. No late homework will be accepted; the lowest score will be dropped. You are encouraged to work together, but you must each turn in your own work.
Grading: Homework 30%, midterm 30%, final 40%.
Other important dates: April 9 (last day to add or drop a course), May 7 (last day to withdraw from a course).
Students with disabilities: Please come talk to me no later than the first week of classes.