Probability Spaces and Random Variables

Let Ω be an arbitrary non-empty set and P(Ω) be the aggregate of all its subsets. The class A ⊂ P(Ω) is said to be a Boolean algebra (an algebra), if: (a) Ω ∈ A; (b) A is closed with respect to the operations of union, intersection and complementation; i.e., from A, B ∈ A it follows that A ∪ B ∈ A, AB ∈ A and Ā ∈ A.