Let be a Set. Then a -algebra is a nonempty collection of Subsets of such that the following hold:
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 .
See also Borel Sigma Algebra, Borel Space, Measurable Set, Measurable Space, Measure Algebra, Standard Space