Axiomatic Method of Measure and Integration (VII). Definition and Existence Theorem of LS-measure (Y. Ito, “RS-integral and LS-integral”, Chap.8−9)

In this paper, we define the LS-measure on Rd, (d ≥ 1) by prescribing the complete system of axioms. Then we prove the existence theorem of the LS-measure and we determine all the LS-measures. They are the new results.