An Isomorphism between the Completion of an Algebra and Its Caratheodory Extension
نویسنده
چکیده
Let Ω denote an algebra of sets and μ a σ-finite measure. We then prove that the completion of Ω under the pseudometric d(A,B) = μ∗(A△B) is σ-algebra isomorphic and isometric to the Caratheodory Extension of Ω under the equivalence relation ∼.
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تاریخ انتشار 2008