# STA 6466: Assignments

• Assignment 1 (Due Sep 08): Billingsley, exercises 2.3, 2.4, 2.9, 2.11, 2.12.
• Assignment 2 (Due Sep 15): Billingsley, exercises 2.13, 2.17, 3.11, 10.1, 10.2.
• Assignment 3 (Due Sep 29): Billingsley, exercises 2.19, 3.3(a-d,f), 3.12, 11.2. Also do exercise 1.3.1 in the notes (concerning an alternative construction of the completion of a measure space).
• Assignment 4 (Due Oct 13): Billingsley, exercises 12.1(just the one-dimensional case), 13.8, 13.9. Also do the additional exercises given here.
Note: For 12.1 you will need Cauchy's equation from the appendix (A.20).
• Assignment 5 (Due Nov 14): Billingsley 16.2, 16.3, 16.4, 17.6, 17.7.
• Assignment 6 (Due Nov 21): Billingsley 18.4, 18.6, 18.10 (a), 18.13.
Note:
• In 18.4, why is E a product-measurable set? This question is easy to answer, but exercise 18.2 should give you pause for thought.
• Don't forget to do the measurability part of 18.6.
• Part (b) of 18.10 was done in class.
• I suppose there's a measurability question to be answered in 18.13 too, but it's also easy (as in 18.4).
There are many other interesting exercises in Billingsley. Some you may wish to try are given below. I will add to this list as we go along.
• 2.1, 2.5(b), 2.18
• 3.13, 3.19
• 10.3
• 11.3
• 12.11
• 13.1, 13.2(a,c), 13.6, 13.10, 13.11, 13.12, 13.14
• 16.1, 16.8
• 17.4, 17.8
• 18.1, 18.2, 18.3, 18.8, 18.9, 18.11, 18.14