The first part of this article is in the preceding volume of the same review. Here in this part the author discusses the definitions and properties of measurable space, measurable function and Lebesgue-Stieltjes integral. The relation between probability space and induced probability space is made precise. The author's conclusion is that the construction of probability space is tightly connected with our conceptual scheme of analyzing data and that the probability space has properties of mathematical model, therefore its fitness is to be tested empirically and there is no a priori criterion to judge which one is the best.