Abstract
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 {Bλ : λ ∈ Λ} ⊂ B the least upper bound is denoted by ⋁λ B λ and the greatest lower bound by Λλ B λ. The latter, Λλ B λ, is the same as the set-theoretic intersection ∩λ B λ but the former, ⋁λ B λ, is not the set-theoretic union ∪λ B λ but the σ-algebra generated by the union.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Itô, K. (2004). Preliminaries. In: Barndorff-Nielsen, O.E., Sato, Ki. (eds) Stochastic Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10065-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-10065-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05805-9
Online ISBN: 978-3-662-10065-3
eBook Packages: Springer Book Archive