Let X be a set and let {Fi | i ∈ I} be an arbitrary collection of σ- algebras. Showthat the collection F := {F | ∀i ∈ I, F ∈ Fi} is a σ-algebra.
Question
Solution 1
To show that F is a σ-algebra, we need to verify three properties:
- The empty set and X are in F.
- If A is in F, then its complement is in F.
- If {An} is a countable collection of sets in F, then the union of {An} is in F.
Let's verify each property:
- Since each Fi is a σ-algebra, the emp Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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