Erschienen in:

2004 | OriginalPaper | Buchkapitel

Preliminaries

verfasst von : Kiyosi Itô

Erschienen in: Stochastic Processes

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

Zugang erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Let (Ω,B,P) be the basic probability space. The family B of all sub-σ-algebras of ß is a complete lattice with respect to the usual set-theoretic inclusion relation.₁ For {B_λ : λ ∈ Λ} ⊂ B the least upper bound is denoted by ⋁_λB_λ and the greatest lower bound by Λ_λB_λ. The latter, Λ_λB_λ, is the same as the set-theoretic intersection ∩_λB_λ but the former, ⋁_λB_λ, is not the set-theoretic union ∪_λ B_λ but the σ-algebra generated by the union.

Springer Professional