Professor: Katy Craig, katy•craig at ucsb • edu

Lecture: Tuesday and Thursday, 2-3:15pm, Girvitz, Room 1116

Office Hours: Wednesdays 2-3pm and Thursdays 12:45-1:45pm in SH 6507

Textbook: Folland, Real Analysis: Modern Techniques and Their Applications, second edition

Other Recommended References:

Exams: There will be two midterms and one final exam. The examinations will be closed book and closed note. There will be no retaking or rescheduling exams under any circumstances, as the grading scheme allows you to drop your lowest midterm score.

First Midterm: October 23rd, 2-3:15pm
Second Midterm: November 20th, 2-3:15pm
Final Exam: Tuesday, December 9th, 4-7pm

Homework:

Homework will be due Sundays at 11:59pm.
Assignments will be posted on this website and submitted via Gradescope.
Only problems marked with an asterisk (*) should be submitted for grading.
At least one problem on each of the exams will be chosen from the non-asterisked homework problems.
No late homework will be accepted.
The lowest two homework grades will be dropped and will not count toward the final grade.
Regarding collaboration/Google/AI:
- The solutions to most homework problems can be found on the internet. The purpose of homework is to practice solving problems. Don’t miss out on that practice, or you will deprive yourself of key preparation for the exams.
- Discussing homework problems with classmates is an excellent way to learn the material. However, be aware that it's easy to overestimate how much you actually understand individually when you solve problems in a group.

Participation: Participation will be based on attendance and contributions during lecture. If you have personal circumstances that make it difficult for you to attend lecture, please contact me within the first two weeks of classes to make an alternative arrangement.

Grading Scheme:

Participation: 5%, Homework: 30%, Highest of Two Midterm Grades 30%, Final 35%
All regrade requests must be received within two weeks after the graded work is returned.
This is a core course for MATH and STSAP graduate students. Grades of A- or better will mean that you are performing at the Ph.D. level. Grades of B and B+ indicate performance at the MA level.

Prerequisites: undergraduate level real analysis, similar to UCSB 118abc

Outline of Course:

Part I: Measures	Part II: Integration
sigma-algebras	measurable functions
measures	integration of functions
outer measures	modes of convergence
Lebesgue measure	product measures

Weekly Plan:

		topic	reading	due soon	notes
1	Sept 25 (Th)	introduction to measures	1.1	Office Hours Poll	LEC1
2	Sept 30 (T)	sigma-algebras and measures	1.2-1.3		LEC2
3	Oct 2 (Th)	outer measures	1.4	HW1, HW1SOL	LEC3
4	Oct 7 (T)	Borel measures on the real line (I)	1.5		LEC4
5	Oct 9 (Th)	Borel measures on the real line (II)		HW2, HW2tex	LEC5
6	Oct 14 (T)	Borel measures on the real line (III)
7	Oct 16 (Th)	measurable functions	2.1	HW3, HW3tex
8	Oct 21 (T)	integration of nonnegative functions (I)	2.2
9	Oct 23 (Th)	first midterm, over lectures 1-7
10	Oct 28 (T)	integration of nonnegative functions (II)
11	Oct 30 (Th)	integration of real valued functions	2.3
12	Nov 4 (T)	modes of convergence (I)	2.4
13	Nov 6 (Th)	modes of convergence (II)
14	Nov 11 (T)	modes of convergence (III)
15	Nov 13 (Th)	product measures (I)	1.2, 2.5
16	Nov 18 (T)	product measures (II)
17	Nov 20 (Th)	second midterm, over lectures 1-14
	Nov 25 (T)	no class
18	Dec 2 (T)	product measures (III) - Fubini-Tonelli
19	Dec 4 (Th)	n-dimensional Lebesgue measure	2.6
20	Dec 5 (F)	optional review session, time TBD
	Dec 9 (T)	final exam, 4-7pm

Acknowledgements: I would like to thank Chuck Akemann and Davit Harutyunyan for sharing their materials from previous sessions of math 201A at UCSB. I would also like to acknowledge Eric Carlen (Rutgers) and Brian White (Stanford), from whom I learned measure theory. I have referred the materials from their courses in preparing this one.