Assignments

End of semester

• I have collected all homework assignments into a single file for quick reference. Also, for future lecturers, here is the .tex source file.
• Moreover, I have prepared a shorter list of review problems. Here are the .pdf file and the .tex source file for future lecturers.

First week

• Read/review sections 1.1, 1.2, 1.3 in the official textbook.
• Read/review sections 2.1, 2.2, 2.3 in the official textbook.

Second week

Third week

• Solve the following problems. There will be more added next week.

Fourth week

• Read from Tao's book the part of the preface regarding infinite sums: start with Remark 0.0.1 and finish with the proof of Theorem 0.0.2 (Tonelli's theorem for series) — we will use this theorem in class.
• Solve the following problems.

Fifth week

• Solve the following problems. The solution to the very last problem on the additivity of the Lebesgue outer measure for compact sets is here.

Sixth week

Seventh week

• Solve the following problems.
• Write carefully the detailed solutions to the previous assignment – as mentioned in class, even after gathering the ideas for solving a problem in measure theory, writing down its solution may be a difficult task, this process being similar at first with that of learning a new language. It is very important that you become fluent in this new language, and this takes practice. Bring your notes to the exercise class on Tuesday and show them to me or present them on the blackboard (try not to feel intimidated by this, you can always choose not to show your work).

Eighth week

Ninth week

Tenth week

Eleventh week

• Solve the following problems.
• Write down neatly the solutions to problems 4, 6, 7 and bring them to me next Tuesday. I will read your solutions and then make comments so you may improve your writing.
• Read the proof of Egorov's theorem (Theorem 1.3.26 in Tao's book) on your own and try to understand the argument.

Twelfth week

Thirteenth week

• Solve the following problems.
• Review on your own some of the basic concepts in calculus, as mentioned in class (the beginning of section 1.6 in Tao's book). Pay attention to the proofs, as you may have not studied them very carefully in calculus.