ABSTRACT
If readers have been looking closely at how the author proves the properties of Riemann and Riemann - Stieltjes integration, they will have noted that the proofs are intimately tied to the way the author uses partitions to divide the function domain into small pieces. In this chapter, the author is now going to explore a new way to associate a given bounded function with a real number which can be interpreted as the integral. He now discusses a very important sigma-algebra of subsets of the real line called the Bord sigma-algebra. The author wishes to explore what properties the composition of a continuous function and a measurable function might have. To handle the composition of a continuous function and an extended real-valued measurable function, he needs an approximation result. The author handles the case of the composition of a continuous function and an extended real-valued measurable function.
