#### 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.

`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`

- Solve the following problems.

`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`

`Sixth week`

- Solve the following problems.

`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`

- Solve the following problems.

`Ninth week`

- Solve the following problems.

`Tenth week`

- Solve the following problems.

`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`

- Solve the following problems.

`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.