Abstract
This chapter focuses on the Stieltjes integral. The various concepts of integral play a large part in the application of mathematical analysis to present-day science. If there are two sets A1 and A2, consisting of objects of any type, elements, then the sets are said to have the same power if a one-to-one correspondence can be established between the elements of A1 and the elements of A2, that is, a correspondence in which a definite element of A2 is associated with each element of A1 and conversely, each element of A2 is associated with one and only one element of A1. An infinite set, that is, a set containing an infinite number of elements, is described as denumerable if it has the same power as the set of all positive integers, that is, if its elements can be enumerated by means of positive integers: a1, a2, a3. Two denumerable sets have the same power. The chapter discusses Darboux sums and the Stieltjes integral of a continuous function. Various theorems are also proven in the chapter.
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