Let be a set. Then a -algebra is a nonempty collection of subsets of such that the following hold:
1. is in .
2. If is in , then so is the complement of .
3. If is a sequence of elements of , then the union of the s is in .
If is any collection of subsets of , then we can always find a -algebra containing , namely the power set of . By taking the intersection of all -algebras containing , we obtain the smallest such -algebra. We call the smallest -algebra containing the -algebra generated by .