- #1
azdang
- 84
- 0
Homework Statement
I have to create the smallest sigma-algebra where [tex]\Omega[/tex] is the union of disjoint sets Ai, i=1,2,...,n.
Now, I did this for the case where [tex]\Omega[/tex] is just the union of disjoint sets A_1 and A_2, and found that the sigma-algebra would be {[tex]\Omega[/tex], {}, A_1, A_2} since A_1 is the complement of A_2 and vice versa.
So for the A_i's, would the sigma algebra just be {[tex]\Omega[/tex], {}, A_1, A_2,...,A_n, [tex]\Omega[/tex]-A_1, [tex]\Omega[/tex]-A_2,...,[tex]\Omega[/tex]-A_n}?
Thank you! :)