ABSTRACT
The purpose of this chapter is to consider some of the main theorems in probability which are closely related to measure theory and Lebesgue integration. This section is on random vectors and random variables, random vectors with values in ℝ or ℂ. We will denote by F either ℂ or ℝ with the understanding that F = ℂ unless specified otherwise. In dealing with random vectors, we will need to consider the integral of a vector valued function. This is easy to do by considering it componentwise. Thus, if ν is a measure on a σ algebra of sets of Ω and
