We characterize the measurable spaces (Ω,A) such that, for each sub-σ-field G of A and each decreasing filtered family (F_t) of sub-σ-fields of A, with F_t ↓ F_∞, we have F_t ∨ G ↓ F_∞ ∨ G. It follows a characterization of the probability spaces (Ω, A, P) such that, for each sub-σ-field G of A and each decreasing sequence (F_n) of sub-σ-fields of A, with F_n ↓ F_∞, we have ⋂_n (F_n ∨ G) ∼ F_∞ ∨ G (mod P).

Sur l'interversion de l'ordre entre deux opérations sur les tribus

Crimaldi I;
2007-01-01

Abstract

We characterize the measurable spaces (Ω,A) such that, for each sub-σ-field G of A and each decreasing filtered family (F_t) of sub-σ-fields of A, with F_t ↓ F_∞, we have F_t ∨ G ↓ F_∞ ∨ G. It follows a characterization of the probability spaces (Ω, A, P) such that, for each sub-σ-field G of A and each decreasing sequence (F_n) of sub-σ-fields of A, with F_n ↓ F_∞, we have ⋂_n (F_n ∨ G) ∼ F_∞ ∨ G (mod P).
2007
sigma-fields; martingales
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/3649
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