Atomic Intersection of Σ-fields and Some of Its Consequences
نویسندگان
چکیده
Let (Ω,F , P ) be a probability space. For each G ⊂ F , define G as the σ-field generated by G and those sets F ∈ F satisfying P (F ) ∈ {0, 1}. Conditions for P to be atomic on ∩i=1Ai, with A1, . . . ,Ak ⊂ F sub-σ-fields, are given. Conditions for P to be 0-1-valued on ∩i=1Ai are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expectations and the intersection property.
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