A algebra on is a family such that If is a family of sets in then Alternatively, is a -algebra if it is a pi-system and a d-system. Remark If you allow only finite unions in 3. then is called an Algebra. algebra are countable unions. Definition (Generated -algebra) Let be a set of subsets of . Define Then is a -algebra which is called the -algebra generated by . It is the smallest -algebra containing Dynkin’s pi-system Lemma