This set is due Feb. 8 at the beginning of lecture. Of course, let me know if more time is needed or anything like that.
0. During lecture I have sometimes skipped some arguments or not given as much detail as you may have wanted. If there was a result that in particular required of you some effort to complete in detail, please state it here and show me how you filled in the gaps left in lecture. Also, if there is a result for which you do not see how to fill in the details, let me know as well, as I may have overlooked something and it may be worth going back over it in class.
1. Give an example of a bounded set 
does not exist.
2. Compute ![m^{*,(J)}({\mathbb Q}\cap[0,1])](https://s0.wp.com/latex.php?latex=m%5E%7B%2A%2C%28J%29%7D%28%7B%5Cmathbb+Q%7D%5Ccap%5B0%2C1%5D%29&bg=ffffff&fg=333333&s=0&c=20201002)
3. From the book, solve exercises 1.1.3, 1.1.5, 1.1.6, and 1.1.15.
[To get you started on 1.1.3: First verify in 
![m'((0,1/n))\le m'([0,1])/n](https://s0.wp.com/latex.php?latex=m%27%28%280%2C1%2Fn%29%29%5Cle+m%27%28%5B0%2C1%5D%29%2Fn&bg=ffffff&fg=333333&s=0&c=20201002)
![m'([0,1]^n)](https://s0.wp.com/latex.php?latex=m%27%28%5B0%2C1%5D%5En%29&bg=ffffff&fg=333333&s=0&c=20201002)
Note we essentially solved 1.1.15 in class, but under the assumption that 1.1.6 holds.]
4. From the book, solve Exercises 1.1.7-10. Make sure to explain in 1.1.9 why Tao’s definition of compact convex polytopes coincides with what should be our intuitive definition. Please also verify that convex polytopes are indeed convex.
(For a nice argument verifying that indeed 
5. From the book, solve exercise 1.1.11.
(If you are not comfortable with linear algebra beyond size 
6. From the book, solve exercise 1.1.13.
7. From the book, solve exercise 1.1.17.
A kind of library 
(I have added a missing prime in the hint on question 3.) Thanks to Tara for noticing it.