Axiomatic Method of Measure and Integration (V). Definition and Existence Theorem of the RS-measure (Yoshifumi Ito, “RS-integral and LS-integral”, Chapter 3)

In this paper, we define the RS-measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the existence theorem of the RS-measure and determine all the RS-measures. This is a new result.