ABSTRACT
Definition 2.1.1. Let (Ω ,F ,P) be a probability space. A transformation X from (Ω ,F) to a measurable space (X ,A) is called an X -valued random variable if X−1(A) ∈F for all A ∈A. In case X =Rn, the Euclidean space and A = B (Rn), then X will be referred to as an n-random vector. For n = 1, we call X a real-valued random variable (or just a random variable). A vector
X = (X1, ...,Xn) is an n-random vector if and only if X1,X2,⋯,Xn are random variables.
