Construction of a Lattice on the Completion Space of an Algebra and an Isomorphism to Its Caratheodory Extension
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چکیده
In this paper, we will show how one is able to construct a lattice on the completion of an algebra and to obtain an isomorphism to its Caratheodory Extension. In addition, it will be shown that the lattice form a σ-algebra and a complete Heyting algebra of countable type.
منابع مشابه
An Isomorphism between the Completion of an Algebra and Its Caratheodory Extension
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 2009