**Announcements:**

- (June 10) Grades available here. Solutions available here.
- (June
6) A typo in Q3(b): f should be assumed to lie in L^2( B_* ), not L^2( B
). Also, in Q5, the hypothesis should
be that
*all*sufficiently high order derivatives of lambda vanish, not just a single derivative. Again, the version on the web page contains the fix. - (June 3) There is an error in Q4 of the final; the definition of weak convergence given is not correct. The question should instead ask for a sequence mu_{j_k} which converges to mu whenever integrated against a continuous, compactly supported function f. The version on the web page contains the fix.
- (Mar 28) The take-home final is available here. I have changed the due date to the last day of classes June 10, as I will be traveling starting on June 13.
- (Mar 7) Some notes on the Marcinkiewicz interpolation theorem.

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**Instructor**: Terence Tao, tao@math.ucla.edu, x64844, MS 5622

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**Lecture: **MWF 12-12:50, MS 5148

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**Discussion section: **No discussion section
for this course.

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**Office Hours**: W 2-3

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**TA:** No TA for this course.

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**TA Office hours:** No TA for this course.

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**Textbook**: Folland, Real Analysis, Second
Edition, Wiley Interscience 1999, ISBN 0471317160. We will cover Chapters 6,7,9; some variation
from this plan may develop depending on time constraints. (Fourier analysis,
while important, is covered separately in 247AB). Familiarity with the preceding material (Ch
1-5 from Folland) is assumed; this should not be a problem if you have already
taken 245AB. Note that a current list of
errata to this text is maintained here
(thanks to Julia Garibaldi for pointing this out).

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**Prerequisite**: Math 245AB (or
equivalent). In particular, students
should be familiar with the Lebesgue integral, point set topology, and Banach
spaces.

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**Grading**: There will be a take-home final,
handed out in ninth week of class, which will determine your final grade (A, B,
or C).

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**Reading**** Assignment**: You should read Chapters
1-5 if you have not already encountered this material. Of course, you should also be reading the
sections covered in lecture (and homework) concurrently with the course.

·
**Homework**: This homework is optional (and
will not be accepted or graded), but is strongly recommended

1. Suggested homework for week 1: Chapter 6, Questions 3, 5, 9, 14, 18, 21

2. Suggested homework for week 2: Chapter 6, Questions 27, 31, 32, 33

3. Suggested homework for weeks 3-4: Chapter 6, Questions 38, 40, 43, 45

4. Suggested homework for weeks 5-6: Chapter 7, Questions 1, 2, 10, 12, 13

5. Suggested homework for week 7: Chapter 7, Questions 17, 22; Chapter 9, Questions 1, 2, 3, 6, 11, 15

6. Suggested homework for weeks 8-9: Chapter 7, Questions 19, 20, 22, 23, 25