Completions of ranked spaces and their applications to the study of nonabsolute integrals (Q1314669)

The author gives a survey on the theory of ranked spaces due to \textit{K. Kunugi} [Proc. Japan Acad. 30, 553-556 (1954; Zbl 0057.14702)] and of their completions [Math. Japon. 23, 409-422 (1978; Zbl 0401.54024)]. As application, he presents definitions of the \(A\)-integral [the author Proc. Japan Acad. 44, 133-138, 225-230 (1968; Zbl 0159.34701), 44, 904- 909 (1968; Zbl 0167.32702); 45, 86-91 (1969; Zbl 0179.35703); 45, 374-379 (1969; Zbl 0182.07903)] and of the Denjoy integrals in the restricted sense [Math. Japon. 37, No. 1, 89-101 (1992; Zbl 0764.26004)].