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Home / Shakarchi and Stein Measure Theory Solutions Chapter 3

Shakarchi and Stein Measure Theory Solutions Chapter 3

131 C - Topics in Analysis: Measure Theory - Spring 2013 - UCLA

Back.

Time: 11am MWF for lectures and 11am T for discussion.
Place:

Lectures: MS 5137. Discussion: MS 5137.

E-mail:

antieau@math.ucla.edu.
Phone: 310-825-3068.
Course webpage: www.math.ucla.edu/~antieau/201302-131c.html.
Course discussion site: piazza.com.

Office hours: 12-1 MF and 1-2 W in my office,

MS 6617D.
TA: Ben Krause (benkrause23@math.ucla.edu).
TA office hours: TBA.

Book: Stein and Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, ISBN: 0-691-11386-6. We will cover chapters 1 and 2, and parts of chapters 4-6.

Important dates:

  • 5/27 - Memorial Day. No class.
  • 6/11 - Final exam. The final will be a cumulative take-home exam and will be due at 5:00pm on Friday 14 June.

Problem sets:
  • Set 1 - Due 4/16 - Exercises from Chapter 1: 1, 4, 9-11, 13, 16, 22, 33, 35, 36. Problems from Chapter 1: 1, 5.
  • Set 2 - Due 5/7 - Exercises from Chapter 2: 2, 5, 6, 7, 9, 10, 11, 12, 16, 20, 21. Problem from Chapter 2: 3.
  • Set 3 - Due 5/21 - Exercises from Chapter 4: 2, 4, 5, 7, 8, 9, 11, 12. Problem from Chapter 4: 1.
  • Set 4 - Due 6/7 - Exercises 3: 1, 4. Exercises from Chapter 4: 30, 31. Exercises from Chapter 5: 1, 2. Exercises from Chapter 6: 16, 17, 21, 24. Problem from Chapter 6: 6.

Evaluation:
  • The final raw score will be computed with the following weights: 60% problem sets and 40% final.
  • You can work collectively on the homework, but not on the final. You can also look to other sources for solutions. However, you must cite any outside source you have used in finding your solution. And, you must write up your solution in your own words.
  • I suggest you make a serious attempt at each problem before consulting a peer or another text. A serious attempt means thinking for at least an hour about the problem.
  • This class is about measure theory, but it is also about continuing to learn how to write good, even perfect, proofs. Thus, grading will be based on correctness and presentation. Both are required to receive an A. Good presentation means that your proofs should be written to the same standard as those in the textbook. This includes for instance writing in full sentences, correct use of quantifiers, and correct disposal of cases.
  • This might require you to write and rewrite your solutions.
  • Each problem will be graded with a score from 1 to 4.
    • 4 - Perfect proof. Correct and written to the standard of the text.
    • 3 - Logically correct proof, although the presentation leaves something to be desired.
    • 2 - Good idea for a proof, but with some missed cases or false statements. Otherwise, good presentation.
    • 1 - Some idea for a proof, but largely incorrect, with poor presentation.
    Roughly speaking, I expect an A grade will mean mostly 4s, a B+ grade mostly 3s and a B grade mostly 2s.
  • A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including the midterm, but who, for a legitimate, documented reason, miss the final.
Piazza:
  • I encourage everyone to use the free discussion board piazza.com for discussion of the class. You may go to the website and enroll in MATH 131C. This is a site that allows everyone to ask and answer questions. It is my hope that you will help each other out on the site. If there are questions about policies, exams, etc, please post them on piazza as well. I will answer them there so that the answers will be public and useful to other students.
  • However, please look at previous questions and this syllabus before posting a new question. In other words, RTFM.
  • You may post anonymously, for reference.
  • You may give us anonymous feedback by posting a private note on piazza.
Miscellanea:
  • If you wish to request an accommodation due to a disability, please contact the Office for Students with Disabilities as soon as possible at A255 Murphy Hall, (310) 825-1501, (310) 206-6083 (telephone device for the deaf). Website: www.osd.ucla.edu.
  • This class will use the myUCLA gradebook facility.
  • Come to office hours!

Catalogue description: 131C. Topics in Analysis. (4) Lecture, three hours; discussion, one hour. Requisites: courses 131A-131B. Advanced topics in analysis, such as Lebesgue integral, integration on manifolds, harmonic analysis. Content varies from year to year. May be repeated for credit by petition.

Shakarchi and Stein Measure Theory Solutions Chapter 3

Source: https://math.northwestern.edu/~antieau/201302-131c.html