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- W1971763024 abstract "Let $${(Omega, mathcal{F}, P)}$$ be a probability space. For each $${mathcal{G}subsetmathcal{F}}$$ , define $${overline{mathcal{G}}}$$ as the σ-field generated by $${mathcal{G}}$$ and those sets $${Fin mathcal{F}}$$ satisfying $${P(F)in{0,1}}$$ . Conditions for P to be atomic on $${cap_{i=1}^koverline{mathcal{A}_i}}$$ , with $${mathcal{A }_1,ldots,mathcal{A}_ksubsetmathcal{F}}$$ sub-σ-fields, are given. Conditions for P to be 0-1-valued on $${cap_{i=1}^k overline{mathcal{A}_i}}$$ are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expectations and the intersection property." @default.
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- W1971763024 date "2009-06-10" @default.
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- W1971763024 title "Atomic intersection of σ-fields and some of its consequences" @default.
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- W1971763024 doi "https://doi.org/10.1007/s00440-009-0230-x" @default.
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