ABSTRACT
Preliminaries. Let (Ω,F , P ) be a probability space, R = [−∞,+∞] denote the extended real line and B(R) and B(Rn) the Borel σ-fields on R and Rn respectively.
A random object on (Ω,F , P ) is a measurable map X : (Ω,F , P ) → (Ω1,F1) with values in some measurable space (Ω1,F1). PX denotes the distribution of X (appendix B.5). If Q is any probability on (Ω1,F1) we write X ∼ Q to indicate that PX = Q. If (Ω1,F1) = (Rn,B(Rn)) respectively (Ω1,F1) = (R,B(R)), X is called a random vector respectively random variable. In particular random variables are extended real valued.
