In the previous paper, 1955, we have shown some conditions characterizing the Denjoy's special integral, and we have presented, from the point of view of successive approximation shown in those conditions, a multidimensional integration, which is called integral(D) in, based on the derivation in the strong sense, in such a way that: the fundamental theorem of the calculus and the Fubini's theorem hold for the integral. From the same point of view, in this paper we present multidimensional integrals based on the derivation in the regular sense.
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