ABSTRACT
In Example 19.2 and Problem 19.8, the functions we considered have infinitely many discontinuities. The function in Problem 19.8 is Riemann integrable, whereas the function in Example 19.2 is not Riemann integrable. The natural question which we will answer in this chapter is what type of infinitely many discontinuities a function may have to remain Riemann integrable. For this, we need the following definitions and elementary results.
