MATH 245C : Real Analysis


  • (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.

        Instructor: Terence Tao,, x64844, MS 5622

        Lecture: MWF 12-12:50, MS 5148

        Discussion section: No discussion section for this course.

        Office Hours: W 2-3

        TA: No TA for this course.

        TA Office hours: No TA for this course.

        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).

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

        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).

        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