Preliminaries

Abstract

For each interval I in ${I\!\!R}$ = (–∞, ∞) let $\mathcal{B}$ (I) denote the σ-field of Borel subsets of I. For each t ∈ ${I\!\!R}$ ₊= [0, ∞), let $\mathcal{B}$ _t denote $\mathcal{B}$([0, t]) and let $\mathcal{B}$ denote $\mathcal{B}({I\!\!R}_{+})=\bigvee \nolimits_{t \in {{I\!\!R}}_{+}} \mathcal{B}_{t}$ — the smallest σ-field containing $\mathcal{B}$ _t for all t in ${I\!\!R}$ ₊.