Axiomatic Method of Measure and Integration (II). Definition of the Riemann Integral and its Fundamental Properties (Yoshifumi Ito “Differential and Integral Calculus II”, Chapter 9)

In this paper, we define the Riemann integral of the Jordan measurable function on Rd, (d ≥ 1).
Then we study the method of calculation of the Riemann integral. Further we clarify the convergence properties of the Riemann integral completely. These facts are the new results.