Let be a set.
Then, is a σ-algebra on the set if the following is true:
- ( is an element of .)
- (For any set, if a set is an element of , then its complement is in also.)
- (If there is a countable collection of sets that are elements of , then the union of those elements are also in ).
If is a σ-algebra on the set , then is a measure space.