prove that an arbitrary intersection of σ-algebras is a σ-algebra, i.e. let {A_α} where α is in I (indexing set) be a collection of σ-algebras on a given set Ω. Prove that A=intersection {A_α}(where α is in I)
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I dont know topology but I think proving 2 and 3 is easy. Since they follow directly from set properties...A subset Σ of the power set of a set X is a σ-algebra if and only if it has the following properties:
- Σ is nonempty
- If E is in Σ then so is the complement (X \ E) of E.
- The union of countably many sets in Σ is also in Σ.
Which axiom are you having trouble with?