If X is any set, then the family consisting only of the empty set and X is a σ-algebra over X, the so-called trivial σ-algebra. Another σ-algebra over X is given by the full power set of X. The collection of subsets of X which are countable or whose complements are countable is a σ-algebra, which is distinct from the powerset of X iff X is uncountable.
If {Σa} is a family of σ-algebras over X, then the intersection of all Σa ...
If X is any set, then the family consisting only of the empty set and X is a σ-algebra over X, the so-called trivial σ-algebra. Another σ-algebra over X is given by the full power set of X. If X is uncountable then the family of all E contained in X where E or the complement X-E is countable forms a σ-algebra.
If {Σa} is a family of σ-algebras over X, then the intersection of all Σa ...
