For ten points, identify this  rst rigorously-de ned integral.
This process is performed with respect to the Jordan measure, and can only be performed on an indicator function of a set if that set is Jordan measurable. This process is generalized by a similarly named one called the  gauge  one, and it cannot be performed on any function which has more than countably many points at which it is discontinuous. This process is equivalent to a similar process named for   Darboux, and the Lebesgue monotone convergence theorem fails to hold for this process. This process uses tagged partitions in order to compute intermediate values, which are called  sums  and named for the same person as this process. For ten points, identify this  rst rigorously-de ned integral.
This process is performed with respect to the Jordan measure, and can only be performed on an indicator function of a set if that set is Jordan measurable.
Riemann integral [accept word forms, prompt on Darboux integral before  Darboux , prompt on integral before read]