Exercises, due Wed Sept 3.

From Jacod and Protter, problems 2.6, 2.7, 2.10 and 2.14.

2.6 Let be a -algebra of subsets of and let . Show that is a -algebra of subsets of . Is this still true if is a subset of that is not a member of ?

2.7 Let be a function mapping to another space with a -algebra . Let . Show that is a -algebra on .

2.10 Using the definition of a probability measure, show that if , then .

2.14 Suppose that and . Show that .