Recent content by standardgirl

so, F = empty set, {1,2,3,4}, {3,4,5,6}, {1,2,3,4,5,6}? where under countable union, you can get: empty set, {1,2,3,4}, {3,4,5,6}, {1,2,3,4,5,6} which are all elements of F. Then in this case, X(w) is not measurable, because the preimage of 7 ={5,6} is not a set in F?

so F = empty set U {1,2,3,4} U {3,4,5,6} instead of F ={empty set, 1,2,3,4,5,6} ? ps. I need to have this problem done by tonight since it's due tomorrow morning (US time). :smile:

A sigma-albegra F over the set X is a subsets of X which is closed under contable set operations. The empty set is in F. If E is in F, then the complement of E is also in F. If E1, E2, ..., En is a sequence in F, then their contable union is also in F. This is the def. of sigma-algebra in my...

Thank you for the reply, but I still don't know what I need to do. Anyone else has any idea? thank you.

Let S={1,2,3,4,5,6}, F=σ(A1,A2), ie., the σ-algebra generated by A1 and A1 (the smallest σ-algebra containing A1 and A2) with A1={1,2,3,4} and A2={3,4,5,6}. Please complete the following: a. List all sets in F b. Is the random variable X(w)= 2, w=1,2,3,4; X(w)=7, w=5,6 measurable w.r.t. F...