Sigma-Algebra

Definition: A sigma-algebra is a collection of sets that satisfy certain properties with respect to their union. (Intuitively, the collection must include any result of complementations, unions, and intersections of its elements. The effect is to define properties of a collection of sets such that one can define probability on them in a consistent way.) Formally:

Let S be a set and A be a collection of subsets of S. A is a sigma-algebra of S if:

1. the null set and S itself are members of A
2. the complement of any set in A is also in A
3. countable unions of sets in A are also in A.

It follows from these that a sigma-algebra is closed under countable complementation, unions, and intersections.

(Econterms)

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